Journal of Inequalities in Pure and Applied Mathematics
|
|
- Leonard Bernard Lambert
- 5 years ago
- Views:
Transcription
1 Journal of Inequalities in Pure and Applied Mathematics THE METHOD OF LOWER AND UPPER SOLUTIONS FOR SOME FOURTH-ORDER EQUATIONS ZHANBING BAI, WEIGAO GE AND YIFU WANG Department of Applied Mathematics, Beijing Institute of Technology, Beijing , People s Republic of China. baizhanbing@263.net volume 5, issue 1, article 13, Received 17 September, 2003; accepted 23 January, Communicated by: A.M. Fink Abstract Home Page c 2000 Victoria University ISSN (electronic):
2 Abstract In this paper, by combining a new maximum principle of fourth-order equations with the theory of eigenline problems, we develop a monotone method in the presence of lower and upper solutions for some fourth-order ordinary differential equation boundary value problem. Our results indicate there is a relation between the existence of solutions of nonlinear fourth-order equation and the first eigenline of linear fourth-order equation Mathematics Subject Classification: 34B15, 34B10. Key words: Maximum principle; Lower and upper solutions; Fourth-order equation. This work is sponsored by the National Nature Science Foundation of China ( ) and the Doctoral Program Foundation of Education Ministry of China ( ). The authors thank the referees for their careful reading of the manuscript and useful suggestions. 1 Introduction Maximum Principle The Monotone Method References Page 2 of 17
3 1. Introduction This paper consider solutions of the fourth-order boundary value problem (1.1) u (4) (x) = f(x, u(x), u (x)), 0 < x < 1, (1.2) u(0) = u(1) = u (0) = u (1) = 0, where f : [0, 1] R R R is continuous. Many authors [1] [8], [10], [11], [13] [17] have studied this problem. In [1, 4, 6, 8, 10, 16], Aftabizadeh et al. showed the existence of positive solution to (1.1) (1.2) under some growth conditions of f and a non-resonance condition involving a two-parameter linear eigenvalue problem. These results are based upon the Leray Schauder continuation method and topological degree. In [2, 5, 7, 11, 15], Agarwal et al. considered an equation of the form u (4) (x) = f(x, u(x)), with diverse kind of boundary conditions by using the lower and upper solution method. Recently, Bai [3] and Ma et al. [14] developed the monotone method for the problem (1.1) (1.2) under some monotone conditions of f. More recently, with using Krasnosel skii fixed point theorem, Li [13] showed the existence results of positive solutions for the following problem u (4) + βu αu = f(t, u), 0 < t < 1, Page 3 of 17
4 u(0) = u(1) = u (0) = u (1) = 0, where f : [0, 1] R + R + is continuous, α, β R and β < 2π 2, α β 2 /4, α/π 4 + β/π 2 < 1. In this paper, by the use of a new maximum principle of fourth-order equation and the theory of the eigenline problem, we intend to further relax the monotone condition of f and get the iteration solution. Our results indicate there exists some relation between the existence of positive solutions of nonlinear fourth-order equation and the first eigenline of linear fourth-order equation. Page 4 of 17
5 2. Maximum Principle In this section, we prove a maximum principle for the operator L : F C[0, 1] defined by Lu = u (4) au + bu. Here a, b R satisfy (2.1) u F and a π + b 2 π + 1 > 0, 4 a2 4b 0, a > 2π 2 ; F = {u C 4 [0, 1] u(0) = 0, u(1) = 0, u (0) 0, u (1) 0}. Lemma 2.1. [12] Let f(x) be continuous for a x b and let c < λ 1 = π 2 /(b a) 2. Let u satisfies u (x) + cu(x) = f(x), u(a) = u(b) = 0. for x (a, b), Assume that u(x 1 ) = u(x 2 ) = 0 where a x 1 < x 2 b and u(x) 0 for x 1 x x 2. If either f(x) 0 for all x [x 1, x 2 ] or f(x) 0 for all x [x 1, x 2 ] and f(x) is not identically zero on [x 1, x 2 ], then u(x)f(x) 0 for all x [x 1, x 2 ]. Lemma 2.2. If u(x) satisfies u + cu(x) 0, for x (a, b) u(a) 0, u(b) 0, where c < λ 1 = π 2 /(b a) 2. Then u(x) 0, in [a, b]. Page 5 of 17
6 Proof. It follows by Lemma 2.1. Lemma 2.3. If u F satisfies Lu 0, then u 0 in [0, 1]. Proof. Set Ax = x. As a, b R satisfy (2.1), we have that Lu = u (4) au + bu = (A r 2 )(A r 1 )u 0, where r 1,2 = (a ± a 2 4b)/2 π 2. In fact, r 1 = (a + a 2 4b)/2 r 2 = (a a 2 4b)/2. By a/π 2 + b/π > 0, we have aπ 2 + b + π 4 > 0, thus a 2 + 4aπ 2 + 4π 4 > a 2 4b, because a 2 4b 0, so (a + 2π 2 ) 2 > ( a 2 4b) 2. Combining this together with a > 2π 2, we can conclude a + 2π 2 > a 2 4b. Then, r 1 r 2 = (a a 2 4b)/2 > π 2. Let y = (A r 1 )u = u r 1 u, then i.e., On the other hand, u F yields that (A r 2 )y 0, y r 2 y 0. (2.2) y(0) = u (0) r 1 u(0) 0, y(1) = u (1) r 1 u(1) 0. Page 6 of 17
7 Therefore, by the use of Lemma 2.2, there exists i.e., y(x) 0, x [0, 1], u (x) r 1 u(x) = y(x) 0. This together with Lemma 2.2 and the fact that u(0) = 0, that u(x) 0 in [0, 1]. Remark 2.1. Observe that a, b R satisfies (2.1) if and only if (2.3) b 0, or a π + b 2 π + 1 > 0, a > 4 2π2 ; (2.4) b > 0, a > 0, a 2 4b 0; u(1) = 0 implies or (2.5) b > 0, 0 > a > 2π 2, a π + b 2 π + 1 > 0, 4 a2 4b 0. From (2.3) and (2.4), we can easily conclude r 1 = a + a 2 4b 0. 2 Therefore, (2.2) can be obtained under u(0) 0, u(1) 0, u (0) 0, u (1) 0, and F can be defined as F = {u C 4 [0, 1] u(0) 0, u(1) 0, u (0) 0, u (1) 0}, we refer the reader to [3, 13]. Page 7 of 17
8 Lemma 2.4. [7] Given (a, b) R 2, the following problem (2.6) (2.7) u (4) au + bu = 0, u(0) = u(1) = u (0) = u (1) = 0, has a non-trivial solution if and only if for some k N. a (kπ) + b 2 (kπ) + 1 = 0, 4 Page 8 of 17
9 3. The Monotone Method In this section, we develop the monotone method for the fourth order two-point boundary value problem (1.1) (1.2). For given a, b R satisfying a/π 2 +b/π 4 +1 > 0, a 2 4b 0, a > 2π 2 and f : [0, 1] R R R, let (3.1) f 1 (x, u, v) = f(x, u, v) + bu av. Then (1.1) is equal to (3.2) Lu = f 1 (x, u, u ). Definition 3.1. Letting α C 4 [0, 1], we say that α is an upper solution for the problem (1.1) (1.2) if α satisfies α (4) (x) f(x, α(x), α (x)), for x (0, 1), α(0) = 0, α(1) = 0, α (0) 0, α (1) 0. Definition 3.2. Letting β C 4 [0, 1], we say β is a lower solution for the problem (1.1) (1.2) if β satisfies β (4) (x) f(x, β(x), β (x)), for x (0, 1), β(0) = 0, β(1) = 0, β (0) 0, β (1) 0. Page 9 of 17
10 Remark 3.1. If a, b satisfy (2.3) or (2.4), the boundary values can be replaced by α(0) 0, α(1) 0; β(0) 0, β(1) 0. It is clear that if α, β are upper and lower solutions of the problem (1.1) (1.2) respectively, α, β are upper and lower solutions of the problem (3.2) (1.2) respectively, too. Theorem 3.1. If there exist α and β, upper and lower solutions, respectively, for the problem (1.1) (1.2) which satisfy (3.3) β α and β + r(α β) α, and if f : [0, 1] R R R is continuous and satisfies (3.4) f(x, u 2, v) f(x, u 1, v) b(u 2 u 1 ), for β(x) u 1 u 2 α(x), v R, and x [0, 1]; (3.5) f(x, u, v 2 ) f(x, u, v 1 ) a(v 2 v 1 ), for v 2 + r(α β) v 1, α r(α β) v 1, v 2 β + r(α β), u R, and x [0, 1], where a, b R satisfy a/π 2 + b/π > 0, a 2 4b 0, a > 2π 2 and r = (a a 2 4b)/2, then there exist two monotone sequences {α n } and {β n }, non-increasing and non-decreasing, respectively, with α 0 = α and β 0 = β, which converge uniformly to the extremal solutions in [β, α] of the problem (1.1) (1.2). Page 10 of 17
11 Proof. Consider the problem (3.6) u (4) (x) au (x) + bu(x) = f 1 (x, η(x), η (x)), for x (0, 1), (3.7) u(0) = u(1) = u (0) = u (1) = 0, with η C 2 [0, 1]. Since a/π 2 + b/π > 0, with the use of Lemma 2.4 and Fredholm Alternative [9], the problem (3.6) (3.7) has a unique solution u. Define T : C 2 [0, 1] C 4 [0, 1] by (3.8) T η = u. Now, we divide the proof into three steps. Step 1. We show (3.9) T C C. Here, C = {η C 2 [0, 1] β η α, α r(α β) η β + r(α β)} is a nonempty bounded closed subset in C 2 [0, 1]. In fact, for ζ C, set ω = T ζ. By the definition of α, β and C, combining (3.1), (3.4), and (3.5), we have that (3.10) (α ω) (4) (x) a(α ω) (x) + b(α ω)(x) f 1 (x, α(x), α (x)) f 1 (x, ζ(x), ζ (x)) = f(x, α(x), α (x)) f(x, ζ(x), ζ (x)) 0, a(α ζ) (x) + b(α ζ)(x) Page 11 of 17
12 (3.11) (α ω)(0) = 0, (α ω)(1) = 0, (3.12) (α ω) (0) 0, (α ω) (1) 0. With the use of Lemma 2.3, we obtain that α ω. Analogously, there holds ω β. By the proof of Lemma 2.3, combining (3.10), (3.11), and (3.12), we have that (α ω) (x) r(α ω)(x) 0, x (0, 1), hence, ω (x) + r(α β)(x) ω (x) + r(α ω)(x) α (x), for x (0, 1), i.e., Analogously, Thus, (3.9) holds. ω (x) α (x) r(α β)(x), for x (0, 1). ω (x) β (x) + r(α β)(x), for x (0, 1). Step 2. Let u 1 = T η 1, u 2 = T η 2, where η 1, η 2 C satisfy η 1 η 2 and η r(α β) η 2. We show (3.13) u 1 u 2, u 1 + r(α β) u Page 12 of 17
13 In fact, by (3.4), (3.5), and the definition of u 1, u 2, L(u 2 u 1 )(x) = f 1 (x, η 2 (x), η 2(x)) f 1 (x, η 1 (x), η 1(x)) 0, (u 2 u 1 )(0) = (u 2 u 1 )(1) = 0, (u 2 u 1 ) (0) = (u 2 u 1 ) (1) = 0. With the use of Lemma 2.3, we get that u 1 u 2. Similar to Step 1, we can easily prove u 1 + r(α β) u 2. Thus, (3.13) holds. Step 3. The sequences {α n } and {β n } are obtained by recurrence: α 0 = α, β 0 = β, α n = T α n 1, β n = T β n 1, n = 1, 2,.... From the results of Step 1 and Step 2, we have that (3.14) β = β 0 β 1 β n α n α 1 α 0 = α, (3.15) β = β 0, α = α 0, α r(α β) α n, β n β +r(α β). Moreover, from the definition of T (see (3.8)), we get i.e., α n (4) (x) aα n(x) + bα n (x) = f 1 (x, α n 1 (x), α n 1(x)), α n (4) (x) = f 1 (x, α n 1 (x), α n 1(x)) + aα n(x) bα n (x) (3.16) f 1 (x, α n 1 (x), α n 1(x)) + a[β + r(α β)](x) bβ(x), Page 13 of 17
14 (3.17) α n (0) = α n (1) = α n(0) = α n(1) = 0. Analogously, β n (4) (x) = f 1 (x, β n 1 (x), β n 1(x)) + aβ n(x) bβ n (x) (3.18) f 1 (x, β n 1 (x), β n 1(x)) + a[β + r(α β)](x) bβ(x), (3.19) β n (0) = β n (1) = β n(0) = β n(1) = 0. From (3.14), (3.15), (3.16), and the continuity of f 1, we have that there exists M α,β > 0 depending only on α and β (but not on n or x) such that (3.20) α (4) n (x) M α,β, for all x [0, 1]. Using the boundary condition (3.17), we get that for each n N, there exists ξ n (0, 1) such that (3.21) α n (ξ n ) = 0. This together with (3.20) yields (3.22) α n (x) = α n (ξ n ) + x ξ n α (4) n (s)ds M α,β. Page 14 of 17
15 By combining (3.15) and (3.17), we can similarly get that there is C α,β > 0 depending only on α and β (but not on n or x) such that (3.23) α n(x) C α,β, for all x [0, 1], (3.24) α n(x) C α,β, for all x [0, 1]. Thus, from (3.14), (3.22), (3.23), and (3.24), we know that {α n } is bounded in C 3 [0, 1]. Similarly, {β n } is bounded in C 3 [0, 1]. Now, by using the fact that {α n } and {β n } are bounded in C 3 [0, 1], we can conclude that {α n }, {β n } converge uniformly to the extremal solutions in [0, 1] of the problem (3.2) (1.2). Therefore, {α n }, {β n } converge uniformly to the extremal solutions in [0, 1] of the problem (1.1) (1.2), too. Example 3.1. Consider the boundary value problem (3.25) u (4) (x) = 5u (x) (u(x) + 1) 2 + sin 2 πx + 1, (3.26) u(0) = u(1) = u (0) = u (1) = 0. It is clear that the results of [3, 7, 13, 14] can t apply to the example. On the other hand, it is easy to check that α = sin πx, β = 0 are upper and lower solutions of (3.25) (3.26), respectively. Letting a = 5, b = 4, then all assumptions of Theorem 3.1 are fulfilled. Hence the problem (3.25) (3.26) has at least one solution u, which satisfies 0 u sin πx. Page 15 of 17
16 References [1] A.R. AFTABIZADEH, Existence and uniqueness theorems for fourthorder boundary value problems, J. Math. Anal. Appl., 116 (1986), [2] R.P. AGARWAL, On fourth-order boundary value problems arising in beam analysis, Differential Integral Equations, 2 (1989), [3] Z.B. BAI, The Method of lower and upper solutions for a bending of an elastic beam equation, J. Math. Anal. Appl., 248 (2000), [4] Z.B. BAI AND H.Y. WANG, On the positive solutions of some nonlinear fourth-order beam equations, J. Math. Anal. Appl., 270 (2002), [5] A. CABADA, The method of lower and upper solutions for second, third, fourth and higher order boundary value problems, J. Math. Anal. Appl., 185 (1994), [6] C. DE COSTER, C. FABRY AND F. MUNYAMARERE, Nonresonance conditions for fourth-order nonlinear boundary value problems, Internat. J. Math. Sci., 17 (1994), [7] C. DE COSTER AND L. SANCHEZ, Upper and lower solutions, Ambrosetti-Prodi problem and positive solutions for fourth-order O. D. E., Riv. Mat. Pura Appl., 14 (1994), [8] M.A. DEL PINO AND R.F. MANASEVICH, Existence for a fourth-order boundary value problem under a two parameter nonresonance condition, Proc. Amer. Math. Soc., 112 (1991), Page 16 of 17
17 [9] D. GILBARG AND N.S. TRUDINGER, Elliptic Partial Differential Equations of Second-Order, Springer Verlag, New York, [10] C.P. GUPTA, Existence and uniqueness theorem for a bending of an elastic beam equation, Appl. Anal., 26 (1988), [11] P. KORMAN, A maximum principle for fourth-order ordinary differential equations, Appl. Anal., 33 (1989), [12] A.C. LAZER AND P.J. MCKENNA, Global bifurcation and a theorem of Tarantello, J. Math. Anal. Appl., 181 (1994), [13] Y.X. LI, Positive solutions of fourth-order boundary value problems with two parameters, J. Math. Anal. Appl., 281 (2003), [14] R.Y. MA, J.H. ZHANG AND S.M. FU, The method of lower and upper solutions for fourth-order two-point boundary value problems, J. Math. Anal. Appl., 215 (1997), [15] J. SCHRODER, Fourth-order two-point boundary value problems; estimates by two side bounds, Nonl. Anal., 8 (1984), [16] R.A. USMANI, A uniqueness theorem for a boundary value problem, Proc. Amer. Math. Soc., 77 (1979), [17] Q.L. YAO AND Z.B. BAI, Existence of positive solutions of boundary value problems for u (4) (t) λh(t)f(u(t)) = 0, Chinese. Ann. Math. Ser. A, 20 (1999), [In Chinese] Page 17 of 17
Upper and lower solution method for fourth-order four-point boundary value problems
Journal of Computational and Applied Mathematics 196 (26) 387 393 www.elsevier.com/locate/cam Upper and lower solution method for fourth-order four-point boundary value problems Qin Zhang a, Shihua Chen
More informationTRIPLE POSITIVE SOLUTIONS FOR A CLASS OF TWO-POINT BOUNDARY-VALUE PROBLEMS
Electronic Journal of Differential Equations, Vol. 24(24), No. 6, pp. 8. ISSN: 72-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) TRIPLE POSITIVE
More informationPERIODIC PROBLEMS WITH φ-laplacian INVOLVING NON-ORDERED LOWER AND UPPER FUNCTIONS
Fixed Point Theory, Volume 6, No. 1, 25, 99-112 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.htm PERIODIC PROBLEMS WITH φ-laplacian INVOLVING NON-ORDERED LOWER AND UPPER FUNCTIONS IRENA RACHŮNKOVÁ1 AND MILAN
More informationMULTIPLICITY OF CONCAVE AND MONOTONE POSITIVE SOLUTIONS FOR NONLINEAR FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS
Fixed Point Theory, 4(23), No. 2, 345-358 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html MULTIPLICITY OF CONCAVE AND MONOTONE POSITIVE SOLUTIONS FOR NONLINEAR FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS
More informationEXISTENCE AND UNIQUENESS OF SOLUTIONS FOR FOURTH-ORDER BOUNDARY-VALUE PROBLEMS IN BANACH SPACES
Electronic Journal of Differential Equations, Vol. 9(9), No. 33, pp. 1 8. ISSN: 17-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu EXISTENCE AND UNIQUENESS
More informationAbdulmalik Al Twaty and Paul W. Eloe
Opuscula Math. 33, no. 4 (23, 63 63 http://dx.doi.org/.7494/opmath.23.33.4.63 Opuscula Mathematica CONCAVITY OF SOLUTIONS OF A 2n-TH ORDER PROBLEM WITH SYMMETRY Abdulmalik Al Twaty and Paul W. Eloe Communicated
More informationA global solution curve for a class of free boundary value problems arising in plasma physics
A global solution curve for a class of free boundary value problems arising in plasma physics Philip Korman epartment of Mathematical Sciences University of Cincinnati Cincinnati Ohio 4522-0025 Abstract
More informationNONLINEAR THREE POINT BOUNDARY VALUE PROBLEM
SARAJEVO JOURNAL OF MATHEMATICS Vol.8 (2) (212), 11 16 NONLINEAR THREE POINT BOUNDARY VALUE PROBLEM A. GUEZANE-LAKOUD AND A. FRIOUI Abstract. In this work, we establish sufficient conditions for the existence
More informationMULTIPLE POSITIVE SOLUTIONS FOR FOURTH-ORDER THREE-POINT p-laplacian BOUNDARY-VALUE PROBLEMS
Electronic Journal of Differential Equations, Vol. 27(27, No. 23, pp. 1 1. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp MULTIPLE POSITIVE
More informationPositive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations
J. Math. Anal. Appl. 32 26) 578 59 www.elsevier.com/locate/jmaa Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations Youming Zhou,
More informationANALYSIS AND APPLICATION OF DIFFUSION EQUATIONS INVOLVING A NEW FRACTIONAL DERIVATIVE WITHOUT SINGULAR KERNEL
Electronic Journal of Differential Equations, Vol. 217 (217), No. 289, pp. 1 6. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ANALYSIS AND APPLICATION OF DIFFUSION EQUATIONS
More informationWITH REPULSIVE SINGULAR FORCES MEIRONG ZHANG. (Communicated by Hal L. Smith) of repulsive type in the sense that G(u)! +1 as u! 0.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 127, Number 2, February 1999, Pages 41{47 S 2-9939(99)512-5 PERIODIC SOLUTIONS OF DAMPED DIFFERENTIAL SYSTEMS WITH REPULSIVE SINGULAR FORCES MEIRONG
More informationUpper and lower solutions method and a fractional differential equation boundary value problem.
Electronic Journal of Qualitative Theory of Differential Equations 9, No. 3, -3; http://www.math.u-szeged.hu/ejqtde/ Upper and lower solutions method and a fractional differential equation boundary value
More informationA NONLINEAR DIFFERENTIAL EQUATION INVOLVING REFLECTION OF THE ARGUMENT
ARCHIVUM MATHEMATICUM (BRNO) Tomus 40 (2004), 63 68 A NONLINEAR DIFFERENTIAL EQUATION INVOLVING REFLECTION OF THE ARGUMENT T. F. MA, E. S. MIRANDA AND M. B. DE SOUZA CORTES Abstract. We study the nonlinear
More informationEXISTENCE OF STRONG SOLUTIONS OF FULLY NONLINEAR ELLIPTIC EQUATIONS
EXISTENCE OF STRONG SOLUTIONS OF FULLY NONLINEAR ELLIPTIC EQUATIONS Adriana Buică Department of Applied Mathematics Babeş-Bolyai University of Cluj-Napoca, 1 Kogalniceanu str., RO-3400 Romania abuica@math.ubbcluj.ro
More informationEXISTENCE AND APPROXIMATION OF SOLUTIONS OF SECOND ORDER NONLINEAR NEUMANN PROBLEMS
Electronic Journal of Differential Equations, Vol. 2005(2005), No. 03, pp. 1 10. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) EXISTENCE
More informationExistence of Multiple Positive Solutions of Quasilinear Elliptic Problems in R N
Advances in Dynamical Systems and Applications. ISSN 0973-5321 Volume 2 Number 1 (2007), pp. 1 11 c Research India Publications http://www.ripublication.com/adsa.htm Existence of Multiple Positive Solutions
More informationPositive Solutions of a Third-Order Three-Point Boundary-Value Problem
Kennesaw State University DigitalCommons@Kennesaw State University Faculty Publications 7-28 Positive Solutions of a Third-Order Three-Point Boundary-Value Problem Bo Yang Kennesaw State University, byang@kennesaw.edu
More informationPositive solutions for singular third-order nonhomogeneous boundary value problems with nonlocal boundary conditions
Positive solutions for singular third-order nonhomogeneous boundary value problems with nonlocal boundary conditions Department of Mathematics Tianjin Polytechnic University No. 6 Chenglin RoadHedong District
More informationA New Proof of Anti-Maximum Principle Via A Bifurcation Approach
A New Proof of Anti-Maximum Principle Via A Bifurcation Approach Junping Shi Abstract We use a bifurcation approach to prove an abstract version of anti-maximum principle. The proof is different from previous
More informationExistence and iteration of monotone positive solutions for third-order nonlocal BVPs involving integral conditions
Electronic Journal of Qualitative Theory of Differential Equations 212, No. 18, 1-9; http://www.math.u-szeged.hu/ejqtde/ Existence and iteration of monotone positive solutions for third-order nonlocal
More informationNontrivial Solutions for Boundary Value Problems of Nonlinear Differential Equation
Advances in Dynamical Systems and Applications ISSN 973-532, Volume 6, Number 2, pp. 24 254 (2 http://campus.mst.edu/adsa Nontrivial Solutions for Boundary Value Problems of Nonlinear Differential Equation
More informationExistence and Multiplicity of Solutions for a Class of Semilinear Elliptic Equations 1
Journal of Mathematical Analysis and Applications 257, 321 331 (2001) doi:10.1006/jmaa.2000.7347, available online at http://www.idealibrary.com on Existence and Multiplicity of Solutions for a Class of
More informationOn intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings
Int. J. Nonlinear Anal. Appl. 7 (2016) No. 1, 295-300 ISSN: 2008-6822 (electronic) http://dx.doi.org/10.22075/ijnaa.2015.341 On intermediate value theorem in ordered Banach spaces for noncompact and discontinuous
More informationMultiplesolutionsofap-Laplacian model involving a fractional derivative
Liu et al. Advances in Difference Equations 213, 213:126 R E S E A R C H Open Access Multiplesolutionsofap-Laplacian model involving a fractional derivative Xiping Liu 1*,MeiJia 1* and Weigao Ge 2 * Correspondence:
More informationEXISTENCE OF SOLUTIONS FOR KIRCHHOFF TYPE EQUATIONS WITH UNBOUNDED POTENTIAL. 1. Introduction In this article, we consider the Kirchhoff type problem
Electronic Journal of Differential Equations, Vol. 207 (207), No. 84, pp. 2. ISSN: 072-669. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu EXISTENCE OF SOLUTIONS FOR KIRCHHOFF TYPE EQUATIONS
More informationExistence of Solutions for a Class of Third Order Quasilinear Ordinary Differential Equations with Nonlinear Boundary Value Problems
Advances in Dynamical Systems and Applications ISSN 973-5321, Volume 3, Number 2, pp. 35 321 (28) http://campus.mst.edu/adsa Existence of Solutions for a Class of Third Order Quasilinear Ordinary Differential
More informationPositive Solutions of Three-Point Nonlinear Second Order Boundary Value Problem
Positive Solutions of Three-Point Nonlinear Second Order Boundary Value Problem YOUSSEF N. RAFFOUL Department of Mathematics University of Dayton, Dayton, OH 45469-236 email:youssef.raffoul@notes.udayton.edu
More informationNonlinear Analysis. Global solution curves for boundary value problems, with linear part at resonance
Nonlinear Analysis 71 (29) 2456 2467 Contents lists available at ScienceDirect Nonlinear Analysis journal homepage: www.elsevier.com/locate/na Global solution curves for boundary value problems, with linear
More informationMONOTONE POSITIVE SOLUTION OF NONLINEAR THIRD-ORDER TWO-POINT BOUNDARY VALUE PROBLEM
Miskolc Mathematical Notes HU e-issn 177-2413 Vol. 15 (214), No. 2, pp. 743 752 MONOTONE POSITIVE SOLUTION OF NONLINEAR THIRD-ORDER TWO-POINT BOUNDARY VALUE PROBLEM YONGPING SUN, MIN ZHAO, AND SHUHONG
More informationA VARIANT OF HOPF LEMMA FOR SECOND ORDER DIFFERENTIAL INEQUALITIES
A VARIANT OF HOPF LEMMA FOR SECOND ORDER DIFFERENTIAL INEQUALITIES YIFEI PAN AND MEI WANG Abstract. We prove a sequence version of Hopf lemma, which is essentially equivalent to the classical version.
More informationXiyou Cheng Zhitao Zhang. 1. Introduction
Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center Volume 34, 2009, 267 277 EXISTENCE OF POSITIVE SOLUTIONS TO SYSTEMS OF NONLINEAR INTEGRAL OR DIFFERENTIAL EQUATIONS Xiyou
More informationMultiple positive solutions for a class of quasilinear elliptic boundary-value problems
Electronic Journal of Differential Equations, Vol. 20032003), No. 07, pp. 1 5. ISSN: 1072-6691. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu login: ftp) Multiple positive
More informationFUNCTIONAL COMPRESSION-EXPANSION FIXED POINT THEOREM
Electronic Journal of Differential Equations, Vol. 28(28), No. 22, pp. 1 12. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) FUNCTIONAL
More informationPOSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT BOUNDARY-VALUE PROBLEM. Ruyun Ma
Electronic Journal of Differential Equations, Vol. 1998(1998), No. 34, pp. 1 8. ISSN: 172-6691. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu (login: ftp) POSITIVE SOLUTIONS
More informationPERIODIC SOLUTIONS FOR A KIND OF LIÉNARD-TYPE p(t)-laplacian EQUATION. R. Ayazoglu (Mashiyev), I. Ekincioglu, G. Alisoy
Acta Universitatis Apulensis ISSN: 1582-5329 http://www.uab.ro/auajournal/ No. 47/216 pp. 61-72 doi: 1.17114/j.aua.216.47.5 PERIODIC SOLUTIONS FOR A KIND OF LIÉNARD-TYPE pt)-laplacian EQUATION R. Ayazoglu
More informationJUNXIA MENG. 2. Preliminaries. 1/k. x = max x(t), t [0,T ] x (t), x k = x(t) dt) k
Electronic Journal of Differential Equations, Vol. 29(29), No. 39, pp. 1 7. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu POSIIVE PERIODIC SOLUIONS
More informationEXISTENCE OF THREE WEAK SOLUTIONS FOR A QUASILINEAR DIRICHLET PROBLEM. Saeid Shokooh and Ghasem A. Afrouzi. 1. Introduction
MATEMATIČKI VESNIK MATEMATIQKI VESNIK 69 4 (217 271 28 December 217 research paper originalni nauqni rad EXISTENCE OF THREE WEAK SOLUTIONS FOR A QUASILINEAR DIRICHLET PROBLEM Saeid Shokooh and Ghasem A.
More informationA generalized Fucik type eigenvalue problem for p-laplacian
Electronic Journal of Qualitative Theory of Differential Equations 009, No. 18, 1-9; htt://www.math.u-szeged.hu/ejqtde/ A generalized Fucik tye eigenvalue roblem for -Lalacian Yuanji Cheng School of Technology
More informationSEMILINEAR ELLIPTIC EQUATIONS WITH DEPENDENCE ON THE GRADIENT
Electronic Journal of Differential Equations, Vol. 2012 (2012), No. 139, pp. 1 9. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu SEMILINEAR ELLIPTIC
More informationON SOME ELLIPTIC PROBLEMS IN UNBOUNDED DOMAINS
Chin. Ann. Math.??B(?), 200?, 1 20 DOI: 10.1007/s11401-007-0001-x ON SOME ELLIPTIC PROBLEMS IN UNBOUNDED DOMAINS Michel CHIPOT Abstract We present a method allowing to obtain existence of a solution for
More informationAN EXISTENCE-UNIQUENESS THEOREM FOR A CLASS OF BOUNDARY VALUE PROBLEMS
Fixed Point Theory, 13(2012), No. 2, 583-592 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html AN EXISTENCE-UNIQUENESS THEOREM FOR A CLASS OF BOUNDARY VALUE PROBLEMS M.R. MOKHTARZADEH, M.R. POURNAKI,1 AND
More informationPositive Solutions of Operator Equations and Nonlinear Beam Equations with a Perturbed Loading Force
Positive Solutions of Operator Equations Nonlinear Beam Equations with a Perturbed Loading Force WEN-XIA WANG Taiyuan Normal University Department of Mathematics Taiyuan 312 P. R. China wwxgg@126.com XI-LAN
More informationExistence and Uniqueness of Anti-Periodic Solutions for Nonlinear Higher-Order Differential Equations with Two Deviating Arguments
Advances in Dynamical Systems and Applications ISSN 973-531, Volume 7, Number 1, pp. 19 143 (1) http://campus.mst.edu/adsa Existence and Uniqueness of Anti-Periodic Solutions for Nonlinear Higher-Order
More informationPositive solutions of BVPs for some second-order four-point difference systems
Positive solutions of BVPs for some second-order four-point difference systems Yitao Yang Tianjin University of Technology Department of Applied Mathematics Hongqi Nanlu Extension, Tianjin China yitaoyangqf@63.com
More informationEXISTENCE OF SOLUTIONS FOR BOUNDARY VALUE PROBLEMS ON INFINITE INTERVALS. We consider the second order nonlinear differential equation
Dynamic Systems and Applications 17 (28) 653-662 EXISTECE OF SOLUTIOS FOR BOUDARY VALUE PROBLEMS O IFIITE ITERVALS İSMAİL YASLA Department of Mathematics, Pamukkale University, Denizli 27, Turkey ABSTRACT.
More informationNONTRIVIAL SOLUTIONS TO INTEGRAL AND DIFFERENTIAL EQUATIONS
Fixed Point Theory, Volume 9, No. 1, 28, 3-16 http://www.math.ubbcluj.ro/ nodeacj/sfptcj.html NONTRIVIAL SOLUTIONS TO INTEGRAL AND DIFFERENTIAL EQUATIONS GIOVANNI ANELLO Department of Mathematics University
More informationThe (CLR g )-property for coincidence point theorems and Fredholm integral equations in modular metric spaces
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 1, No., 17, 38-54 ISSN 137-5543 www.ejpam.com Published by New York Business Global The (CLR g )-property for coincidence point theorems and Fredholm
More informationPositive and monotone solutions of an m-point boundary-value problem
Electronic Journal of Differential Equations, Vol. 2002(2002), No.??, pp. 1 16. ISSN: 1072-6691. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu (login: ftp) Positive and
More informationPositive Solution of a Nonlinear Four-Point Boundary-Value Problem
Nonlinear Analysis and Differential Equations, Vol. 5, 27, no. 8, 299-38 HIKARI Ltd, www.m-hikari.com https://doi.org/.2988/nade.27.78 Positive Solution of a Nonlinear Four-Point Boundary-Value Problem
More informationOn the Computations of Eigenvalues of the Fourth-order Sturm Liouville Problems
Int. J. Open Problems Compt. Math., Vol. 4, No. 3, September 2011 ISSN 1998-6262; Copyright c ICSRS Publication, 2011 www.i-csrs.org On the Computations of Eigenvalues of the Fourth-order Sturm Liouville
More informationEXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS FOR FOURTH-ORDER m-point BOUNDARY VALUE PROBLEMS WITH TWO PARAMETERS
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS Volume 43, Number 4, 213 EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS FOR FOURTH-ORDER m-point BOUNDARY VALUE PROBLEMS WITH TWO PARAMETERS XINAN HAO, NAIWEI XU AND
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics ON A HYBRID FAMILY OF SUMMATION INTEGRAL TYPE OPERATORS VIJAY GUPTA AND ESRA ERKUŞ School of Applied Sciences Netaji Subhas Institute of Technology
More informationSTRONG CONVERGENCE OF AN ITERATIVE METHOD FOR VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS
ARCHIVUM MATHEMATICUM (BRNO) Tomus 45 (2009), 147 158 STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR VARIATIONAL INEQUALITY PROBLEMS AND FIXED POINT PROBLEMS Xiaolong Qin 1, Shin Min Kang 1, Yongfu Su 2,
More informationComputations of Critical Groups at a Degenerate Critical Point for Strongly Indefinite Functionals
Journal of Mathematical Analysis and Applications 256, 462 477 (2001) doi:10.1006/jmaa.2000.7292, available online at http://www.idealibrary.com on Computations of Critical Groups at a Degenerate Critical
More informationOn the role playedby the Fuck spectrum in the determination of critical groups in elliptic problems where the asymptotic limits may not exist
Nonlinear Analysis 49 (2002) 603 611 www.elsevier.com/locate/na On the role playedby the Fuck spectrum in the determination of critical groups in elliptic problems where the asymptotic limits may not exist
More informationExistence of a Positive Solution for a Right Focal Discrete Boundary Value Problem
Existence of a Positive Solution for a Right Focal Discrete Boundary Value Problem D. R. Anderson 1, R. I. Avery 2, J. Henderson 3, X. Liu 3 and J. W. Lyons 3 1 Department of Mathematics and Computer Science,
More informationSOME GENERALIZATION OF MINTY S LEMMA. Doo-Young Jung
J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math. 6(1999), no 1. 33 37 SOME GENERALIZATION OF MINTY S LEMMA Doo-Young Jung Abstract. We obtain a generalization of Behera and Panda s result on nonlinear
More informationNonresonance for one-dimensional p-laplacian with regular restoring
J. Math. Anal. Appl. 285 23) 141 154 www.elsevier.com/locate/jmaa Nonresonance for one-dimensional p-laplacian with regular restoring Ping Yan Department of Mathematical Sciences, Tsinghua University,
More informationNONLINEAR EIGENVALUE PROBLEMS FOR HIGHER ORDER LIDSTONE BOUNDARY VALUE PROBLEMS
NONLINEAR EIGENVALUE PROBLEMS FOR HIGHER ORDER LIDSTONE BOUNDARY VALUE PROBLEMS PAUL W. ELOE Abstract. In this paper, we consider the Lidstone boundary value problem y (2m) (t) = λa(t)f(y(t),..., y (2j)
More informationON THE EXISTENCE OF POSITIVE SOLUTIONS OF HIGHER ORDER DIFFERENCE EQUATIONS. P. J. Y. Wong R. P. Agarwal. 1. Introduction
Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center Volume 10, 1997, 339 351 ON THE EXISTENCE OF POSITIVE SOLUTIONS OF HIGHER ORDER DIFFERENCE EQUATIONS P. J. Y. Wong R. P.
More informationON THE STRUCTURE OF FIXED-POINT SETS OF UNIFORMLY LIPSCHITZIAN MAPPINGS. Ewa Sędłak Andrzej Wiśnicki. 1. Introduction
Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center Volume 30, 2007, 345 350 ON THE STRUCTURE OF FIXED-POINT SETS OF UNIFORMLY LIPSCHITZIAN MAPPINGS Ewa Sędłak Andrzej Wiśnicki
More informationEXISTENCE OF SOLUTIONS FOR CROSS CRITICAL EXPONENTIAL N-LAPLACIAN SYSTEMS
Electronic Journal of Differential Equations, Vol. 2014 (2014), o. 28, pp. 1 10. ISS: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu EXISTECE OF SOLUTIOS
More informationON THE EXISTENCE OF THREE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEM. Paweł Goncerz
Opuscula Mathematica Vol. 32 No. 3 2012 http://dx.doi.org/10.7494/opmath.2012.32.3.473 ON THE EXISTENCE OF THREE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEM Paweł Goncerz Abstract. We consider a quasilinear
More informationarxiv:math/ v1 [math.fa] 20 Feb 2001
arxiv:math/12161v1 [math.fa] 2 Feb 21 Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type H. Bueno and C. Tomei Dep. de Matemática - ICEx, UFMG, Caixa Postal 72, Belo Horizonte,
More informationBanach Algebras of Matrix Transformations Between Spaces of Strongly Bounded and Summable Sequences
Advances in Dynamical Systems and Applications ISSN 0973-532, Volume 6, Number, pp. 9 09 20 http://campus.mst.edu/adsa Banach Algebras of Matrix Transformations Between Spaces of Strongly Bounded and Summable
More informationNONTRIVIAL SOLUTIONS FOR SUPERQUADRATIC NONAUTONOMOUS PERIODIC SYSTEMS. Shouchuan Hu Nikolas S. Papageorgiou. 1. Introduction
Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center Volume 34, 29, 327 338 NONTRIVIAL SOLUTIONS FOR SUPERQUADRATIC NONAUTONOMOUS PERIODIC SYSTEMS Shouchuan Hu Nikolas S. Papageorgiou
More informationOn an initial-value problem for second order partial differential equations with self-reference
Note di Matematica ISSN 113-536, e-issn 159-93 Note Mat. 35 15 no. 1, 75 93. doi:1.185/i15993v35n1p75 On an initial-value problem for second order partial differential equations with self-reference Nguyen
More informationMultiple positive solutions for a nonlinear three-point integral boundary-value problem
Int. J. Open Problems Compt. Math., Vol. 8, No. 1, March 215 ISSN 1998-6262; Copyright c ICSRS Publication, 215 www.i-csrs.org Multiple positive solutions for a nonlinear three-point integral boundary-value
More informationEXISTENCE OF SOLUTIONS OF THE DIRICHLET PROBLEM FOR AN INFINITE SYSTEM OF NONLINEAR DIFFERENTIAL-FUNCTIONAL EQUATIONS OF ELLIPTIC TYPE
Opuscula Mathematica Vol. 25 No. 2 2005 Tomasz. Zabawa EXITENCE OF OLUTION OF THE DIRICHLET PROBLEM FOR AN INFINITE YTEM OF NONLINEAR DIFFERENTIAL-FUNCTIONAL EQUATION OF ELLIPTIC TYPE Abstract. The Dirichlet
More informationBOUNDARY VALUE PROBLEMS OF A HIGHER ORDER NONLINEAR DIFFERENCE EQUATION
U.P.B. Sci. Bull., Series A, Vol. 79, Iss. 4, 2017 ISSN 1223-7027 BOUNDARY VALUE PROBLEMS OF A HIGHER ORDER NONLINEAR DIFFERENCE EQUATION Lianwu Yang 1 We study a higher order nonlinear difference equation.
More informationarxiv: v1 [math.ap] 18 Jan 2019
manuscripta mathematica manuscript No. (will be inserted by the editor) Yongpan Huang Dongsheng Li Kai Zhang Pointwise Boundary Differentiability of Solutions of Elliptic Equations Received: date / Revised
More informationA NONLINEAR NEUTRAL PERIODIC DIFFERENTIAL EQUATION
Electronic Journal of Differential Equations, Vol. 2010(2010), No. 88, pp. 1 8. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu A NONLINEAR NEUTRAL
More informationNONLINEAR FREDHOLM ALTERNATIVE FOR THE p-laplacian UNDER NONHOMOGENEOUS NEUMANN BOUNDARY CONDITION
Electronic Journal of Differential Equations, Vol. 2016 (2016), No. 210, pp. 1 7. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu NONLINEAR FREDHOLM ALTERNATIVE FOR THE p-laplacian
More informationEVANESCENT SOLUTIONS FOR LINEAR ORDINARY DIFFERENTIAL EQUATIONS
EVANESCENT SOLUTIONS FOR LINEAR ORDINARY DIFFERENTIAL EQUATIONS Cezar Avramescu Abstract The problem of existence of the solutions for ordinary differential equations vanishing at ± is considered. AMS
More informationK-DIMENSIONAL NONLOCAL BOUNDARY-VALUE PROBLEMS AT RESONANCE. 1. Introduction In this article we study the system of ordinary differential equations
Electronic Journal of Differential Equations, Vol. 215 (215), No. 148, pp. 1 8. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu K-DIMENSIONAL NONLOCAL
More informationExistence Of Solution For Third-Order m-point Boundary Value Problem
Applied Mathematics E-Notes, 1(21), 268-274 c ISSN 167-251 Available free at mirror sites of http://www.math.nthu.edu.tw/ amen/ Existence Of Solution For Third-Order m-point Boundary Value Problem Jian-Ping
More informationAvailable online at J. Nonlinear Sci. Appl., 10 (2017), Research Article
Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 10 (2017), 2719 2726 Research Article Journal Homepage: www.tjnsa.com - www.isr-publications.com/jnsa An affirmative answer to
More informationPositive Solutions to an N th Order Right Focal Boundary Value Problem
Electronic Journal of Qualitative Theory of Differential Equations 27, No. 4, 1-17; http://www.math.u-szeged.hu/ejqtde/ Positive Solutions to an N th Order Right Focal Boundary Value Problem Mariette Maroun
More informationEIGENVALUE QUESTIONS ON SOME QUASILINEAR ELLIPTIC PROBLEMS. lim u(x) = 0, (1.2)
Proceedings of Equadiff-11 2005, pp. 455 458 Home Page Page 1 of 7 EIGENVALUE QUESTIONS ON SOME QUASILINEAR ELLIPTIC PROBLEMS M. N. POULOU AND N. M. STAVRAKAKIS Abstract. We present resent results on some
More informationEXISTENCE OF NONTRIVIAL SOLUTIONS FOR A QUASILINEAR SCHRÖDINGER EQUATIONS WITH SIGN-CHANGING POTENTIAL
Electronic Journal of Differential Equations, Vol. 2014 (2014), No. 05, pp. 1 8. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu EXISTENCE OF NONTRIVIAL
More informationExistence and multiple solutions for a second-order difference boundary value problem via critical point theory
J. Math. Anal. Appl. 36 (7) 511 5 www.elsevier.com/locate/jmaa Existence and multiple solutions for a second-order difference boundary value problem via critical point theory Haihua Liang a,b,, Peixuan
More informationSufficient conditions for functions to form Riesz bases in L 2 and applications to nonlinear boundary-value problems
Electronic Journal of Differential Equations, Vol. 200(200), No. 74, pp. 0. ISSN: 072-669. URL: http://ejde.math.swt.edu or http://ejde.math.unt.edu ftp ejde.math.swt.edu (login: ftp) Sufficient conditions
More informationFRACTIONAL BOUNDARY VALUE PROBLEMS ON THE HALF LINE. Assia Frioui, Assia Guezane-Lakoud, and Rabah Khaldi
Opuscula Math. 37, no. 2 27), 265 28 http://dx.doi.org/.7494/opmath.27.37.2.265 Opuscula Mathematica FRACTIONAL BOUNDARY VALUE PROBLEMS ON THE HALF LINE Assia Frioui, Assia Guezane-Lakoud, and Rabah Khaldi
More informationCONSEQUENCES OF TALENTI S INEQUALITY BECOMING EQUALITY. 1. Introduction
Electronic Journal of ifferential Equations, Vol. 2011 (2011), No. 165, pp. 1 8. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu CONSEQUENCES OF
More informationA REMARK ON MINIMAL NODAL SOLUTIONS OF AN ELLIPTIC PROBLEM IN A BALL. Olaf Torné. 1. Introduction
Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center Volume 24, 2004, 199 207 A REMARK ON MINIMAL NODAL SOLUTIONS OF AN ELLIPTIC PROBLEM IN A BALL Olaf Torné (Submitted by Michel
More informationHOMOCLINIC SOLUTIONS FOR SECOND-ORDER NON-AUTONOMOUS HAMILTONIAN SYSTEMS WITHOUT GLOBAL AMBROSETTI-RABINOWITZ CONDITIONS
Electronic Journal of Differential Equations, Vol. 010010, No. 9, pp. 1 10. ISSN: 107-6691. UL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu HOMOCLINIC SOLUTIONS FO
More informationA TWO PARAMETERS AMBROSETTI PRODI PROBLEM*
PORTUGALIAE MATHEMATICA Vol. 53 Fasc. 3 1996 A TWO PARAMETERS AMBROSETTI PRODI PROBLEM* C. De Coster** and P. Habets 1 Introduction The study of the Ambrosetti Prodi problem has started with the paper
More informationNontrivial solutions for fractional q-difference boundary value problems
Electronic Journal of Qualitative Theory of Differential Equations 21, No. 7, 1-1; http://www.math.u-szeged.hu/ejqtde/ Nontrivial solutions for fractional q-difference boundary value problems Rui A. C.
More informationFixed point theorems of nondecreasing order-ćirić-lipschitz mappings in normed vector spaces without normalities of cones
Available online at www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 10 (2017), 18 26 Research Article Journal Homepage: www.tjnsa.com - www.isr-publications.com/jnsa Fixed point theorems of nondecreasing
More informationA fixed point theorem for weakly Zamfirescu mappings
A fixed point theorem for weakly Zamfirescu mappings David Ariza-Ruiz Dept. Análisis Matemático, Fac. Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain Antonio Jiménez-Melado Dept.
More informationEXISTENCE OF POSITIVE SOLUTIONS OF A NONLINEAR SECOND-ORDER BOUNDARY-VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
Electronic Journal of Differential Equations, Vol. 215 (215), No. 236, pp. 1 7. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu EXISTENCE OF POSITIVE
More informationOn Systems of Boundary Value Problems for Differential Inclusions
On Systems of Boundary Value Problems for Differential Inclusions Lynn Erbe 1, Christopher C. Tisdell 2 and Patricia J. Y. Wong 3 1 Department of Mathematics The University of Nebraska - Lincoln Lincoln,
More informationPOSITIVE SOLUTIONS FOR NONLOCAL SEMIPOSITONE FIRST ORDER BOUNDARY VALUE PROBLEMS
Dynamic Systems and Applications 5 6 439-45 POSITIVE SOLUTIONS FOR NONLOCAL SEMIPOSITONE FIRST ORDER BOUNDARY VALUE PROBLEMS ERBIL ÇETIN AND FATMA SERAP TOPAL Department of Mathematics, Ege University,
More informationThe Existence of Nodal Solutions for the Half-Quasilinear p-laplacian Problems
Journal of Mathematical Research with Applications Mar., 017, Vol. 37, No., pp. 4 5 DOI:13770/j.issn:095-651.017.0.013 Http://jmre.dlut.edu.cn The Existence of Nodal Solutions for the Half-Quasilinear
More informationMULTIPLE SOLUTIONS FOR THE p-laplace EQUATION WITH NONLINEAR BOUNDARY CONDITIONS
Electronic Journal of Differential Equations, Vol. 2006(2006), No. 37, pp. 1 7. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu ftp ejde.math.txstate.edu (login: ftp) MULTIPLE
More informationSome Integral Inequalities with Maximum of the Unknown Functions
Advances in Dynamical Systems and Applications ISSN 0973-5321, Volume 6, Number 1, pp. 57 69 2011 http://campus.mst.edu/adsa Some Integral Inequalities with Maximum of the Unknown Functions Snezhana G.
More informationLOGARITHMIC CONVEXITY OF EXTENDED MEAN VALUES
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 130, Number 6, Pages 1787 1796 S 0002-9939(01)06275-X Article electronically published on December 20, 2001 LOGARITHMIC CONVEXITY OF EXTENDED MEAN
More informationFUZZY IDEALS OF NEAR-RINGS BASED ON THE THEORY OF FALLING SHADOWS
U.P.B. Sci. Bull., Series A, Vol. 74, Iss. 3, 2012 ISSN 1223-7027 FUZZY IDEALS OF NEAR-RINGS BASED ON THE THEORY OF FALLING SHADOWS Jianming Zhan 1, Young Bae Jun 2 Based on the theory of falling shadows
More informationSUBELLIPTIC CORDES ESTIMATES
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 00, Number 0, Pages 000 000 S 000-9939XX0000-0 SUBELLIPTIC CORDES ESTIMATES Abstract. We prove Cordes type estimates for subelliptic linear partial
More information