Research Article Existence for Nonoscillatory Solutions of Higher-Order Nonlinear Differential Equations
|
|
- Ethel Molly Webster
- 5 years ago
- Views:
Transcription
1 International Scholarly Reearch Network ISRN Mathematical Analyi Volume 20, Article ID 85203, 9 page doi:0.502/20/85203 Reearch Article Exitence for Nonocillatory Solution of Higher-Order Nonlinear Differential Equation Yazhou Tian, 2 and Fanwei Meng 2 Department of Baic Coure, Qingdao Technological Univerity Linyi), Feixian 27300, Shandong, China 2 Department of Mathematic, Qufu Normal Univerity, Qufu 27365, Shandong, China Correpondence hould be addreed to Yazhou Tian, tianyazhou369@63.com Received 8 Augut 20; Accepted 22 September 20 Academic Editor: Z. Dola Copyright q 20 Y. Tian and F. Meng. Thi i an open acce article ditributed under the Creative Common Attribution Licene, which permit unretricted ue, ditribution, and reproduction in any medium, provided the original work i properly cited. The exitence of nonocillatory olution of the higher-order nonlinear differential equation rtxtptxt τ n m Q itf i xt σ i 0, t t 0,wherem,n 2areinteger, τ>0, σ i 0, r,p,q i Ct 0,,R, f i CR, R i, 2,...,m, i tudied. Some new ufficient condition for the exitence of a nonocillatory olution of above equation are obtained for general Q i t i, 2,...,m which mean that we allow ocillatory Q i t i, 2,...,m. In particular, our reult improve eentially and extend ome known reult in the recent reference.. Introduction Conider the higher-order nonlinear neutral differential equation [rtxt Ptxt τ n ] Q i tf i xt σ i 0, t t 0.. With repect to., throughout, we hall aume the following: i m, n 2 are integer, τ>0, σ i 0, ii r, P, Q i Ct 0,,R, rt > 0, f i CR, R, i, 2,...,m. Let ρ max im {τ, σ i }. By a olution of., wemeanafunctionxt Ct ρ,,r for ome t t 0 which ha the property that xtptxt τ C n t,,r and rtxtptxt τ n C t,,r and atifie. on t,. A nontrivial olution of. i called ocillatory if it ha arbitrarily large zero, and, otherwie, it i nonocillatory.
2 2 ISRN Mathematical Analyi The exitence of nonocillatory olution of higher-order nonlinear neutral differential equation received much le attention, which i due mainly to the technical difficultie ariing in it analyi. In 998, Kulenovic and Hadziomerpahic invetigated the exitence of nonocillatory olution of econd-order nonlinear neutral differential equation xt cxt τ Q txt σ Q 2 txt σ 2 0, t t 0, E 0 where c i a contant. In 2006, Zhang and Wang 2 invetigated the econd neutral delay differential equation with poitive and negative coefficient: [ rtxt Ptxt τ ] Q tfxt σ Q 2 tgxt σ 2 0, t t 0, E where τ>0, σ i 0,Q,Q 2 Ct 0,,R,f,g CR, R, xfx > 0, xgx > 0, x / 0. By uing Banach contraction mapping principle, they proved the following theorem which extend the reult in. Theorem A 2, Theorem 2.3. Aume that H f and g atify local Lipchitz condition and xfx > 0, xgx > 0, forx/ 0; H 2 Q i t 0, i, 2, aq t Q 2 t i eventually nonnegative for every a>0; H 3 t t 0 t 0 Q i t/d dt <, i, 2 hold if one of the following two condition i atified: H Pt > eventually, and 0 <P 2 P <P 2 2 <, H 5 Pt < eventually, and <P 2 P <, where P lim up t Pt, P 2 lim inf t Pt,then. ha a nonocillatory olution. In 2007, Zhou 3 tudie the exitence of nonocillatory olution of the following econd-order nonlinear differential equation. [ rtxt Ptxt τ ] Q i tf i xt σ i 0, t t 0, E where f i CR, R i, 2,...,m. By uing Kranoelkii fixed point theorem, they proved the following theorem. Theorem B 3, Theorem. Aume that there exit nonnegative contant c and c 2 uch that c c 2 <, c 2 Pt c. Further, aume that t t 0 t 0 Q i t d dt <, i, 2,...,m..2 Then. ha a bounded nonocillatory olution.
3 ISRN Mathematical Analyi 3 In thi paper, by uing Kranoelkii fixed point theorem and ome new technique, we obtain ome ufficient condition for the exitence of a nonocillatory olution of. for general Q i t i, 2,...,m which mean that we allow ocillatory Q i t i, 2,...,m. Meanwhile, we extend the main reult of 2, Main Reult The following fixed point theorem will be ued to prove the main reult in thi ection. Lemma 2. ee 3, Kranoelkii fixed point theorem. Let X be a Banach pace, let Ω be a bounded cloed convex ubet of X, and let S, S 2 be map of Ω into X uch that S x S 2 y Ω for every pair x, y Ω.IfS i a contraction and S 2 i completely continuou, then the equation S x S 2 x x 2. ha a olution in Ω. Theorem 2.2. Aume that there exit nonnegative contant c and c 2 uch that c c 2 <, < c 2 Pt c <. Further, aume that t t 0 t 0 n 2 Q i t d dt <, i, 2,...,m. 2.2 Then. ha a bounded nonocillatory olution. Proof. By interchanging the order of integral, we note that 2.2 i equivalent to t 0 n 2 Q i t d dt <, i, 2,..., m. 2.3 By 2.3, we chooe T>t 0 ufficiently large uch that T n 2 M Q i u du d < c c 2, 2. where M max c c 2 /2x{ f i x :i m}. Let Ct 0,,R be the et of all continuou function with the norm x up t t0 xt <. Then Ct 0,,R i a Banach pace. We define a bounded, cloed, and convex ubet Ω of Ct 0,,R a follow: Ω { x xt Ct 0,,R : c c 2 xt, t t 0 }
4 ISRN Mathematical Analyi Define two map S and S 2 : Ω Ct 0,,R a follow: 3 c 3c 2 Ptxt τ, t T, S xt S xt, t 0 t T, n t n 2 Q i uf i xu σ i du d, t T, S 2 xt t S 2 xt, t 0 t T. 2.6 i We hall how that for any x, y Ω, S x S 2 y Ω. In fact, x, y Ω,andt T,weget S xt S 2 y ) t 3 c 3c 2 Ptxt τ 3 c 3c 2 t t n 2 c 2 T Q i uf i yu σi ) ) du d n 2 M Q i u du d c 3c 2 c 2 c c 2. Furthermore, we have S xt S 2 y ) t 3 c 3c 2 Ptxt τ n 2 Qi uf i yu σi ) ) du d t 3 c 3c 2 c n 2 M Q i u du d T c 3c 2 c c c 2 c c 2. 2 Hence, c c 2 2 S xt S 2 y ) t, for t t Thu, we have proved that S x S 2 y Ω for any x, y Ω. ii WehallhowthatS i a contraction mapping on Ω. In fact, for x, y Ω and t T, we have S xt S y ) t Pt xt τ yt τ c0 x y, 2.0
5 ISRN Mathematical Analyi 5 where c 0 max{c,c 2 }. Thi implie that S x S y c0 x y. 2. Since 0 <c 0 <, we conclude that S i a contraction mapping on Ω. iii We now how that S 2 i completely continuou. Firt, we will how that S 2 i continuou. Let x k x k t Ω be uch that x k t xt a k. Becaue Ω i cloed, x xt Ω. For t T, we have S 2 x k t S 2 xt t T n 2 n 2 Q i u fi x k u σ i f i xu σ i ) du d Q i u f i x k u σ i f i xu σ i ) du d. 2.2 Since f i x k t σ i f i xt σ i 0ak for i, 2,...,m, by applying the Lebegue dominated convergence theorem, we conclude that lim k S 2 x k t S 2 xt 0. Thi mean that S 2 i continuou. Next, we how that S 2 Ω i relatively compact. It uffice to how that the family of function {S 2 x : x Ω} i uniformly bounded and equicontinuou on t 0,. The uniform boundedne i obviou. For the equicontinuity, according to Levitan reult, weonly need to how that, for any given ε>0, T, can be decompoed into finite ubinterval in uch a way that on each ubinterval all function of the family have change of amplitude le than ε.by2.3, for any ε>0, take T T large enough o that n 2 T M Q i u du d < ε Then, for x Ω, t 2 t T, S 2 xt 2 S 2 xt t 2 n 2 Q i u fi xu σ i ) du d t n 2 n 2 t 2 t n 2 Q i u fi xu σ i M Q i u du d M Q i u du d ) du d 2. < ε 2 ε ε. 2
6 6 ISRN Mathematical Analyi For x Ω, T t <t 2 T, S 2 xt 2 S 2 xt t2 t n 2 Q i uf i xu σ i du d t [ t 2 n 2 t n 2] t 2 t2 n 2 M Q i u du d t n 3! t 2 t ξ n 3 M Q i u du d t 2 t2 n 2 M Q i u du d t n 3! t 2 t n 2 M Q i u du d, T Q i uf i xu σ i du d 2.5 where t <ξ<t 2. Then there exit δ>0 uch that S 2 xt 2 S 2 xt <ε, if 0 <t 2 t <δ. 2.6 For any x Ω, t 0 t <t 2 T, itieaytoeethat S 2 xt 2 S 2 xt 0 <ε. 2.7 Therefore, {S 2 x : x Ω} i uniformly bounded and equicontinuou on t 0,, and hence S 2 Ω i relatively compact. By Lemma 2., there i x 0 Ω uch that S x 0 S 2 x 0 x 0.Itieay to ee that x 0 t i a nonocillatory olution of.. The proof i complete. Theorem 2.3. Aume that < c Pt c 2 < and 2.2 hold. Then. ha a bounded nonocillatory olution. Proof. We chooe poitive contant M,M 2,αuch that c M <α< c 2 M 2. c min{α M c c 2 /c, c 2 M 2 α}. Chooing T>t 0 ufficiently large uch that T n 2 M Q i u du d < c, 2.8 where M max M xm 2 { f i x : i m}.
7 ISRN Mathematical Analyi 7 Let Ct 0,,R be the et a in the proof of Theorem 2.2. We define a bounded, cloed, and convex ubet Ω of Ct 0,,R a follow: Ω{x xt Ct 0,,R : M xt M 2,t t 0 }. 2.9 Define two map S and S 2 : Ω Ct 0,,R a follow: n S 2 xt n 2! α xt τ S xt Pt τ Pt τ, t T, S xt, t 0 t T, Ptτ Q i uf i xu σ i ) du d, t T, tτ t τ n 2 S 2 xt, t 0 t T i We hall how that for any x, y Ω, S x S 2 y Ω. In fact, for every x, y Ω,andt T,weget S xt S 2 y ) t α c c c 2 M, S xt S 2 y ) t α c 2 M 2 c 2 c c 2 M Thu, we have proved that S x S 2 y Ω. Since <c Pt c 2 <, we get that S i a contraction mapping. We alo can prove that {S 2 x : x Ω} i uniformly bounded and equicontinuou on t 0,, and hence S 2 Ω i relatively compact. So by Lemma 2., there i x 0 Ω uch that S x 0 S 2 x 0 x 0.Thati, α x 0 t Pt τ x 0t τ n Pt τ Pt τ t τ n 2 Q i uf i x 0 u σ i du d. tτ 2.22 It i eay to ee that x 0 t i a bounded nonocillatory olution of.. The proof i complete. Theorem 2.. Aume that <c Pt c 2 < and 2.2 hold. Then. ha a bounded nonocillatory olution. Proof. We chooe poitive contant M 3, M, αuch that M c 2 M 3 <α<c M. c min{α M c 2 M 3, c M α}. Chooing T>t 0 ufficiently large uch that
8 8 ISRN Mathematical Analyi T n 2 M Q i u du d < c, 2.23 where M max M3 xm { f i x : i m}. Let Ct 0,,R be the et a in the proof of Theorem 2.2. We define a bounded, cloed, and convex ubet Ω of Ct 0,,R a follow: Ω{x xt Ct 0,,R : M 3 xt M,t t 0 }. 2.2 Define two map S and S 2 : Ω Ct 0,,R a follow: n S 2 xt n 2! α xt τ S xt Pt τ Pt τ, t T, S xt, t 0 t T, Ptτ Q i uf i xu σ i du d, t T, tτ t τ n 2 S 2 xt, t 0 t T i We hall how that for any x, y Ω, S x S 2 y Ω. In fact, for every x, y Ω and t T,weget S xt S 2 y ) t c 2 α M c M 3, S xt S 2 y ) t α c c c M Thu, we have proved that S x S 2 y Ω. Since <c Pt c 2 <, wegets i a contraction mapping. We alo can prove that {S 2 x : x Ω} i uniformly bounded and equicontinuou on t 0,, and, hence, S 2 Ω i relatively compact. So by Lemma 2., there i x 0 Ω uch that S x 0 S 2 x 0 x 0.Thati, α x 0 t Pt τ x 0t τ n Pt τ Pt τ t τ n 2 Q i uf i x 0 u σ i du d. tτ 2.27 It i eay to ee that x 0 t i a bounded nonocillatory olution of.. The proof i complete. Remark 2.5. If we let n 2inTheorem 2.2, we get the Theorem in 3. In the cae where n 2, rt, Theorem 2.2 improve eentially Theorem 2.2 in 5. Remark 2.6. The condition of Theorem 2. relaxing the hypothee H of Theorem 3 in 2.
9 ISRN Mathematical Analyi 9 Remark 2.7. Theorem 2.3 and 2. improve eentially Theorem 3 in 2, we allow that Q i t i, 2,...,m are ocillatory. Acknowledgment Thi reearch wa upported by Natural Science Foundation of Shandong Province of China ZR2009AM0 and ZR2009AQ00 and Doctor of Minitry of Education Reference M. R. S. Kulenovic and S. Hadziomerpahic, Exitence of nonocillatory olution of econd order linear neutral delay equation, Mathematical Analyi and Application, vol. 228, no. 2, pp. 36 8, Z. Y. Zhang and X. X. Wang, The ocillatory and nonocillatory criteria of econd nonlinear neutral equation, Sytem Science and Mathematical Science, vol. 26, no. 3, pp , 2006 Chinee. 3 Y. Zhou, Exitence for nonocillatory olution of econd-order nonlinear differential equation, Mathematical Analyi and Application, vol. 33, no., pp. 9 96, B. M. Levitan, Some quetion of the theory of almot periodic function I, Upekhi Matematichekikh Nauk, vol. 2, no. 5, pp , 97 Ruian. 5 X. Y. Lin, Ocillation of econd-order nonlinear neutral differential equation, Mathematical Analyi and Application, vol. 309, no. 2, pp. 2 52, 2005.
10 Advance in Operation Reearch Hindawi Publihing Corporation Volume 20 Advance in Deciion Science Hindawi Publihing Corporation Volume 20 Applied Mathematic Algebra Hindawi Publihing Corporation Hindawi Publihing Corporation Volume 20 Probability and Statitic Volume 20 The Scientific World Journal Hindawi Publihing Corporation Hindawi Publihing Corporation Volume 20 International Differential Equation Hindawi Publihing Corporation Volume 20 Volume 20 Submit your manucript at International Advance in Combinatoric Hindawi Publihing Corporation Mathematical Phyic Hindawi Publihing Corporation Volume 20 Complex Analyi Hindawi Publihing Corporation Volume 20 International Mathematic and Mathematical Science Mathematical Problem in Engineering Mathematic Hindawi Publihing Corporation Volume 20 Hindawi Publihing Corporation Volume 20 Volume 20 Hindawi Publihing Corporation Volume 20 Dicrete Mathematic Volume 20 Hindawi Publihing Corporation Dicrete Dynamic in Nature and Society Function Space Hindawi Publihing Corporation Abtract and Applied Analyi Volume 20 Hindawi Publihing Corporation Volume 20 Hindawi Publihing Corporation Volume 20 International Stochatic Analyi Optimization Hindawi Publihing Corporation Hindawi Publihing Corporation Volume 20 Volume 20
Research Article Triple Positive Solutions of a Nonlocal Boundary Value Problem for Singular Differential Equations with p-laplacian
Abtract and Applied Analyi Volume 23, Article ID 63672, 7 page http://dx.doi.org/.55/23/63672 Reearch Article Triple Poitive Solution of a Nonlocal Boundary Value Problem for Singular Differential Equation
More informationResearch Article A New Kind of Weak Solution of Non-Newtonian Fluid Equation
Hindawi Function Space Volume 2017, Article ID 7916730, 8 page http://doi.org/10.1155/2017/7916730 Reearch Article A New Kind of Weak Solution of Non-Newtonian Fluid Equation Huahui Zhan 1 and Bifen Xu
More informationTRIPLE SOLUTIONS FOR THE ONE-DIMENSIONAL
GLASNIK MATEMATIČKI Vol. 38583, 73 84 TRIPLE SOLUTIONS FOR THE ONE-DIMENSIONAL p-laplacian Haihen Lü, Donal O Regan and Ravi P. Agarwal Academy of Mathematic and Sytem Science, Beijing, China, National
More informationResearch Article Fixed Points and Stability in Nonlinear Equations with Variable Delays
Hindawi Publihing Corporation Fixed Point Theory and Application Volume 21, Article ID 195916, 14 page doi:1.1155/21/195916 Reearch Article Fixed Point and Stability in Nonlinear Equation with Variable
More informationUnbounded solutions of second order discrete BVPs on infinite intervals
Available online at www.tjna.com J. Nonlinear Sci. Appl. 9 206), 357 369 Reearch Article Unbounded olution of econd order dicrete BVP on infinite interval Hairong Lian a,, Jingwu Li a, Ravi P Agarwal b
More informationComputers and Mathematics with Applications. Sharp algebraic periodicity conditions for linear higher order
Computer and Mathematic with Application 64 (2012) 2262 2274 Content lit available at SciVere ScienceDirect Computer and Mathematic with Application journal homepage: wwweleviercom/locate/camwa Sharp algebraic
More informationMULTIPLE POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR P-LAPLACIAN IMPULSIVE DYNAMIC EQUATIONS ON TIME SCALES
Fixed Point Theory, 5(24, No. 2, 475-486 http://www.math.ubbcluj.ro/ nodeacj/fptcj.html MULTIPLE POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR P-LAPLACIAN IMPULSIVE DYNAMIC EQUATIONS ON TIME SCALES
More informationPacific Journal of Mathematics
Pacific Journal of Mathematic OSCILLAION AND NONOSCILLAION OF FORCED SECOND ORDER DYNAMIC EQUAIONS MARIN BOHNER AND CHRISOPHER C. ISDELL Volume 230 No. March 2007 PACIFIC JOURNAL OF MAHEMAICS Vol. 230,
More informationINITIAL VALUE PROBLEMS OF FRACTIONAL ORDER HADAMARD-TYPE FUNCTIONAL DIFFERENTIAL EQUATIONS
Electronic Journal of Differential Equation, Vol. 205 205), No. 77, pp. 9. ISSN: 072-669. URL: http://ejde.math.txtate.edu or http://ejde.math.unt.edu ftp ejde.math.txtate.edu INITIAL VALUE PROBLEMS OF
More informationOn the Unit Groups of a Class of Total Quotient Rings of Characteristic p k with k 3
International Journal of Algebra, Vol, 207, no 3, 27-35 HIKARI Ltd, wwwm-hikaricom http://doiorg/02988/ija2076750 On the Unit Group of a Cla of Total Quotient Ring of Characteritic p k with k 3 Wanambii
More informationOn mild solutions of a semilinear mixed Volterra-Fredholm functional integrodifferential evolution nonlocal problem in Banach spaces
MAEMAIA, 16, Volume 3, Number, 133 14 c Penerbit UM Pre. All right reerved On mild olution of a emilinear mixed Volterra-Fredholm functional integrodifferential evolution nonlocal problem in Banach pace
More informationc n b n 0. c k 0 x b n < 1 b k b n = 0. } of integers between 0 and b 1 such that x = b k. b k c k c k
1. Exitence Let x (0, 1). Define c k inductively. Suppoe c 1,..., c k 1 are already defined. We let c k be the leat integer uch that x k An eay proof by induction give that and for all k. Therefore c n
More informationDragomir and Gosa type inequalities on b-metric spaces
Karapınar and Noorwali Journal of Inequalitie and Application http://doi.org/10.1186/13660-019-1979-9 (019) 019:9 RESEARCH Open Acce Dragomir and Goa type inequalitie on b-metric pace Erdal Karapınar1*
More informationSTABILITY OF A LINEAR INTEGRO-DIFFERENTIAL EQUATION OF FIRST ORDER WITH VARIABLE DELAYS
Bulletin of Mathematical Analyi and Application ISSN: 1821-1291, URL: http://bmathaa.org Volume 1 Iue 2(218), Page 19-3. STABILITY OF A LINEAR INTEGRO-DIFFERENTIAL EQUATION OF FIRST ORDER WITH VARIABLE
More informationThe Power Series Expansion on a Bulge Heaviside Step Function
Applied Mathematical Science, Vol 9, 05, no 3, 5-9 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/0988/am054009 The Power Serie Expanion on a Bulge Heaviide Step Function P Haara and S Pothat Department of
More informationResearch Article Iterative Schemes for Zero Points of Maximal Monotone Operators and Fixed Points of Nonexpansive Mappings and Their Applications
Hindawi Publihing Corporation Fixed Point Theory and Application Volume 2008, Article ID 168468, 12 page doi:10.1155/2008/168468 Reearch Article Iterative Scheme for Zero Point of Maximal Monotone Operator
More informationGeneral System of Nonconvex Variational Inequalities and Parallel Projection Method
Mathematica Moravica Vol. 16-2 (2012), 79 87 General Sytem of Nonconvex Variational Inequalitie and Parallel Projection Method Balwant Singh Thakur and Suja Varghee Abtract. Uing the prox-regularity notion,
More informationSOME RESULTS ON INFINITE POWER TOWERS
NNTDM 16 2010) 3, 18-24 SOME RESULTS ON INFINITE POWER TOWERS Mladen Vailev - Miana 5, V. Hugo Str., Sofia 1124, Bulgaria E-mail:miana@abv.bg Abtract To my friend Kratyu Gumnerov In the paper the infinite
More informationFebruary 5, :53 WSPC/INSTRUCTION FILE Mild solution for quasilinear pde
February 5, 14 1:53 WSPC/INSTRUCTION FILE Mild olution for quailinear pde Infinite Dimenional Analyi, Quantum Probability and Related Topic c World Scientific Publihing Company STOCHASTIC QUASI-LINEAR
More informationResearch Article An Extension of Cross Redundancy of Interval Scale Outputs and Inputs in DEA
Hindawi Publihing Corporation pplied Matheatic Volue 2013, rticle ID 658635, 7 page http://dx.doi.org/10.1155/2013/658635 Reearch rticle n Extenion of Cro Redundancy of Interval Scale Output and Input
More informationSome Sets of GCF ϵ Expansions Whose Parameter ϵ Fetch the Marginal Value
Journal of Mathematical Reearch with Application May, 205, Vol 35, No 3, pp 256 262 DOI:03770/jin:2095-26520503002 Http://jmredluteducn Some Set of GCF ϵ Expanion Whoe Parameter ϵ Fetch the Marginal Value
More informationA THEOREM OF ROLEWICZ S TYPE FOR MEASURABLE EVOLUTION FAMILIES IN BANACH SPACES
Electronic Journal of Differential Equation, Vol. 21(21, No. 7, pp. 1 5. ISSN: 172-6691. URL: http://ejde.math.wt.edu or http://ejde.math.unt.edu ftp ejde.math.wt.edu (login: ftp A THEOREM OF ROLEWICZ
More informationFlag-transitive non-symmetric 2-designs with (r, λ) = 1 and alternating socle
Flag-tranitive non-ymmetric -deign with (r, λ = 1 and alternating ocle Shenglin Zhou, Yajie Wang School of Mathematic South China Univerity of Technology Guangzhou, Guangdong 510640, P. R. China lzhou@cut.edu.cn
More informationMulti-dimensional Fuzzy Euler Approximation
Mathematica Aeterna, Vol 7, 2017, no 2, 163-176 Multi-dimenional Fuzzy Euler Approximation Yangyang Hao College of Mathematic and Information Science Hebei Univerity, Baoding 071002, China hdhyywa@163com
More informationBeta Burr XII OR Five Parameter Beta Lomax Distribution: Remarks and Characterizations
Marquette Univerity e-publication@marquette Mathematic, Statitic and Computer Science Faculty Reearch and Publication Mathematic, Statitic and Computer Science, Department of 6-1-2014 Beta Burr XII OR
More informationResearch Article A Method to Construct Generalized Fibonacci Sequences
Applied Mathematic Volume 6, Article ID 497594, 6 page http://dxdoiorg/55/6/497594 Reearch Article A Method to Contruct Generalized Fibonacci Sequence Adalberto García-Máynez and Adolfo Pimienta Acota
More informationNULL HELIX AND k-type NULL SLANT HELICES IN E 4 1
REVISTA DE LA UNIÓN MATEMÁTICA ARGENTINA Vol. 57, No. 1, 2016, Page 71 83 Publihed online: March 3, 2016 NULL HELIX AND k-type NULL SLANT HELICES IN E 4 1 JINHUA QIAN AND YOUNG HO KIM Abtract. We tudy
More informationGiven the following circuit with unknown initial capacitor voltage v(0): X(s) Immediately, we know that the transfer function H(s) is
EE 4G Note: Chapter 6 Intructor: Cheung More about ZSR and ZIR. Finding unknown initial condition: Given the following circuit with unknown initial capacitor voltage v0: F v0/ / Input xt 0Ω Output yt -
More informationIEOR 3106: Fall 2013, Professor Whitt Topics for Discussion: Tuesday, November 19 Alternating Renewal Processes and The Renewal Equation
IEOR 316: Fall 213, Profeor Whitt Topic for Dicuion: Tueday, November 19 Alternating Renewal Procee and The Renewal Equation 1 Alternating Renewal Procee An alternating renewal proce alternate between
More informationSTOCHASTIC EVOLUTION EQUATIONS WITH RANDOM GENERATORS. By Jorge A. León 1 and David Nualart 2 CINVESTAV-IPN and Universitat de Barcelona
The Annal of Probability 1998, Vol. 6, No. 1, 149 186 STOCASTIC EVOLUTION EQUATIONS WIT RANDOM GENERATORS By Jorge A. León 1 and David Nualart CINVESTAV-IPN and Univeritat de Barcelona We prove the exitence
More informationOn Uniform Exponential Trichotomy of Evolution Operators in Banach Spaces
On Uniform Exponential Trichotomy of Evolution Operator in Banach Space Mihail Megan, Codruta Stoica To cite thi verion: Mihail Megan, Codruta Stoica. On Uniform Exponential Trichotomy of Evolution Operator
More informationOn the Function ω(n)
International Mathematical Forum, Vol. 3, 08, no. 3, 07 - HIKARI Ltd, www.m-hikari.com http://doi.org/0.988/imf.08.708 On the Function ω(n Rafael Jakimczuk Diviión Matemática, Univeridad Nacional de Luján
More informationTAYLOR POLYNOMIALS FOR NABLA DYNAMIC EQUATIONS ON TIME SCALES
TAYLOR POLYNOMIALS FOR NABLA DYNAMIC EQUATIONS ON TIME SCALES DOUGLAS R. ANDERSON Abtract. We are concerned with the repreentation of polynomial for nabla dynamic equation on time cale. Once etablihed,
More informationTHE HAUSDORFF MEASURE OF SIERPINSKI CARPETS BASING ON REGULAR PENTAGON
Anal. Theory Appl. Vol. 28, No. (202), 27 37 THE HAUSDORFF MEASURE OF SIERPINSKI CARPETS BASING ON REGULAR PENTAGON Chaoyi Zeng, Dehui Yuan (Hanhan Normal Univerity, China) Shaoyuan Xu (Gannan Normal Univerity,
More informationChapter 4. The Laplace Transform Method
Chapter 4. The Laplace Tranform Method The Laplace Tranform i a tranformation, meaning that it change a function into a new function. Actually, it i a linear tranformation, becaue it convert a linear combination
More informationResearch Article New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Negative Coefficients
Abstract and Applied Analysis Volume 2010, Article ID 564068, 11 pages doi:10.1155/2010/564068 Research Article New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive
More information696 Fu Jing-Li et al Vol. 12 form in generalized coordinate Q ffiq dt = 0 ( = 1; ;n): (3) For nonholonomic ytem, ffiq are not independent of
Vol 12 No 7, July 2003 cfl 2003 Chin. Phy. Soc. 1009-1963/2003/12(07)/0695-05 Chinee Phyic and IOP Publihing Ltd Lie ymmetrie and conerved quantitie of controllable nonholonomic dynamical ytem Fu Jing-Li(ΛΠ±)
More informationA SIMPLE NASH-MOSER IMPLICIT FUNCTION THEOREM IN WEIGHTED BANACH SPACES. Sanghyun Cho
A SIMPLE NASH-MOSER IMPLICIT FUNCTION THEOREM IN WEIGHTED BANACH SPACES Sanghyun Cho Abtract. We prove a implified verion of the Nah-Moer implicit function theorem in weighted Banach pace. We relax the
More informationBogoliubov Transformation in Classical Mechanics
Bogoliubov Tranformation in Claical Mechanic Canonical Tranformation Suppoe we have a et of complex canonical variable, {a j }, and would like to conider another et of variable, {b }, b b ({a j }). How
More informationList coloring hypergraphs
Lit coloring hypergraph Penny Haxell Jacque Vertraete Department of Combinatoric and Optimization Univerity of Waterloo Waterloo, Ontario, Canada pehaxell@uwaterloo.ca Department of Mathematic Univerity
More informationConvergence of an Approach for Solving Fredholm Functional Integral Equations
Iranian Journal of Mathematical Science and Informatic Vol. 11, No. 1 (2016), pp 35-46 DOI: 10.7508/imi.2016.01.004 Convergence of an Approach for Solving Fredholm Functional Integral Equation Naer Aghazadeh,
More informationFOURIER SERIES AND PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS
FOURIER SERIES AND PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS Nguyen Thanh Lan Department of Mathematic Wetern Kentucky Univerity Email: lan.nguyen@wku.edu ABSTRACT: We ue Fourier erie to find a neceary
More informationPOINCARE INEQUALITY AND CAMPANATO ESTIMATES FOR WEAK SOLUTIONS OF PARABOLIC EQUATIONS
Electronic Journal of Differential Equation, Vol. 206 (206), No. 204, pp. 8. ISSN: 072-669. URL: http://ejde.math.txtate.edu or http://ejde.math.unt.edu POINCARE INEQUALITY AND CAMPANATO ESTIMATES FOR
More informationEXISTENCE AND UNIQUENESS OF SOLUTIONS FOR CAPUTO-HADAMARD SEQUENTIAL FRACTIONAL ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS
Electronic Journal of Differential Equation, Vol. 207 207), No. 36, pp.. ISSN: 072-669. URL: http://ejde.math.txtate.edu or http://ejde.math.unt.edu EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR CAPUTO-HADAMARD
More informationPrimitive Digraphs with the Largest Scrambling Index
Primitive Digraph with the Larget Scrambling Index Mahmud Akelbek, Steve Kirkl 1 Department of Mathematic Statitic, Univerity of Regina, Regina, Sakatchewan, Canada S4S 0A Abtract The crambling index of
More informationSemilinear obstacle problem with measure data and generalized reflected BSDE
Semilinear obtacle problem with meaure data and generalized reflected BSDE Andrzej Rozkoz (joint work with T. Klimiak) Nicolau Copernicu Univerity (Toruń, Poland) 6th International Conference on Stochatic
More informationMATEMATIK Datum: Tid: eftermiddag. A.Heintz Telefonvakt: Anders Martinsson Tel.:
MATEMATIK Datum: 20-08-25 Tid: eftermiddag GU, Chalmer Hjälpmedel: inga A.Heintz Telefonvakt: Ander Martinon Tel.: 073-07926. Löningar till tenta i ODE och matematik modellering, MMG5, MVE6. Define what
More informationON THE APPROXIMATION ERROR IN HIGH DIMENSIONAL MODEL REPRESENTATION. Xiaoqun Wang
Proceeding of the 2008 Winter Simulation Conference S. J. Maon, R. R. Hill, L. Mönch, O. Roe, T. Jefferon, J. W. Fowler ed. ON THE APPROXIMATION ERROR IN HIGH DIMENSIONAL MODEL REPRESENTATION Xiaoqun Wang
More informationAppendix. Proof of relation (3) for α 0.05.
Appendi. Proof of relation 3 for α.5. For the argument, we will need the following reult that follow from Lemma 1 Bakirov 1989 and it proof. Lemma 1 Let g,, 1 be a continuouly differentiable function uch
More informationMichał Kisielewicz SOME OPTIMAL CONTROL PROBLEMS FOR PARTIAL DIFFERENTIAL INCLUSIONS
Opucula Mathematica Vol. 28 No. 4 28 Dedicated to the memory of Profeor Andrzej Laota Michał Kiielewicz SOME OPTIMAL CONTROL PROBLEMS FOR PARTIAL DIFFERENTIAL INCLUSIONS Abtract. Partial differential incluion
More informationON THE SMOOTHNESS OF SOLUTIONS TO A SPECIAL NEUMANN PROBLEM ON NONSMOOTH DOMAINS
Journal of Pure and Applied Mathematic: Advance and Application Volume, umber, 4, Page -35 O THE SMOOTHESS OF SOLUTIOS TO A SPECIAL EUMA PROBLEM O OSMOOTH DOMAIS ADREAS EUBAUER Indutrial Mathematic Intitute
More informationWELL-POSEDNESS OF A ONE-DIMENSIONAL PLASMA MODEL WITH A HYPERBOLIC FIELD
WELL-POSEDNESS OF A ONE-DIMENSIONAL PLASMA MODEL WITH A HYPERBOLIC FIELD JENNIFER RAE ANDERSON 1. Introduction A plama i a partially or completely ionized ga. Nearly all (approximately 99.9%) of the matter
More informationExistence of Countably Many Positive Solutions for Nonlinear Boundary Value Problems on Time Scales
Appl. Math. Inf. Sci. 8, No. 5, 77-87 4 77 Applied Mathematic & Information Science An International Journal http://dx.doi.org/.785/ami/85 Exitence of Countably Many Poitive Solution for Nonlinear Boundary
More informationConvex Hulls of Curves Sam Burton
Convex Hull of Curve Sam Burton 1 Introduction Thi paper will primarily be concerned with determining the face of convex hull of curve of the form C = {(t, t a, t b ) t [ 1, 1]}, a < b N in R 3. We hall
More informationRELIABILITY OF REPAIRABLE k out of n: F SYSTEM HAVING DISCRETE REPAIR AND FAILURE TIMES DISTRIBUTIONS
www.arpapre.com/volume/vol29iue1/ijrras_29_1_01.pdf RELIABILITY OF REPAIRABLE k out of n: F SYSTEM HAVING DISCRETE REPAIR AND FAILURE TIMES DISTRIBUTIONS Sevcan Demir Atalay 1,* & Özge Elmataş Gültekin
More informationQUENCHED LARGE DEVIATION FOR SUPER-BROWNIAN MOTION WITH RANDOM IMMIGRATION
Infinite Dimenional Analyi, Quantum Probability and Related Topic Vol., No. 4 28) 627 637 c World Scientific Publihing Company QUENCHED LARGE DEVIATION FOR SUPER-BROWNIAN MOTION WITH RANDOM IMMIGRATION
More informationarxiv: v2 [math.nt] 30 Apr 2015
A THEOREM FOR DISTINCT ZEROS OF L-FUNCTIONS École Normale Supérieure arxiv:54.6556v [math.nt] 3 Apr 5 943 Cachan November 9, 7 Abtract In thi paper, we etablih a imple criterion for two L-function L and
More informationOne Class of Splitting Iterative Schemes
One Cla of Splitting Iterative Scheme v Ciegi and V. Pakalnytė Vilniu Gedimina Technical Univerity Saulėtekio al. 11, 2054, Vilniu, Lithuania rc@fm.vtu.lt Abtract. Thi paper deal with the tability analyi
More informationKERNEL-RESOLVENT RELATIONS FOR AN INTEGRAL EQUATION
Ø Ñ Å Ø Ñ Ø Ð ÈÙ Ð Ø ÓÒ DOI: 1.478/v117-11-3-7 Tatra Mt. Math. Publ. 48 (11), 5 4 KERNEL-RESOLVENT RELATIONS FOR AN INTEGRAL EQUATION Theodore A. Burton ABSTRACT. Weconideracalarintegralequationz(t) =
More informationConvergence criteria and optimization techniques for beam moments
Pure Appl. Opt. 7 (1998) 1221 1230. Printed in the UK PII: S0963-9659(98)90684-5 Convergence criteria and optimization technique for beam moment G Gbur and P S Carney Department of Phyic and Atronomy and
More informationMulticolor Sunflowers
Multicolor Sunflower Dhruv Mubayi Lujia Wang October 19, 2017 Abtract A unflower i a collection of ditinct et uch that the interection of any two of them i the ame a the common interection C of all of
More informationOSCILLATIONS OF A CLASS OF EQUATIONS AND INEQUALITIES OF FOURTH ORDER * Zornitza A. Petrova
МАТЕМАТИКА И МАТЕМАТИЧЕСКО ОБРАЗОВАНИЕ, 2006 MATHEMATICS AND EDUCATION IN MATHEMATICS, 2006 Proceeding of the Thirty Fifth Spring Conference of the Union of Bulgarian Mathematician Borovet, April 5 8,
More informationResearch Article Existence and Uniqueness of Smooth Positive Solutions to a Class of Singular m-point Boundary Value Problems
Hindawi Publishing Corporation Boundary Value Problems Volume 29, Article ID 9627, 3 pages doi:.55/29/9627 Research Article Existence and Uniqueness of Smooth Positive Solutions to a Class of Singular
More informationLong-term returns in stochastic interest rate models
Long-term return in tochatic interet rate model G. Deeltra F. Delbaen Vrije Univeriteit Bruel Departement Wikunde Abtract In thi paper, we oberve the convergence of the long-term return, uing an extenion
More informationAssignment for Mathematics for Economists Fall 2016
Due date: Mon. Nov. 1. Reading: CSZ, Ch. 5, Ch. 8.1 Aignment for Mathematic for Economit Fall 016 We now turn to finihing our coverage of concavity/convexity. There are two part: Jenen inequality for concave/convex
More informationResearch Article Simplicity and Commutative Bases of Derivations in Polynomial and Power Series Rings
ISRN Agebra Voume 2013 Artice ID 560648 4 page http://dx.doi.org/10.1155/2013/560648 Reearch Artice Simpicity and Commutative Bae of Derivation in Poynomia and Power Serie Ring Rene Batazar Univeridade
More informationChapter 7: The Laplace Transform Part 1
Chapter 7: The Laplace Tranform Part 1 王奕翔 Department of Electrical Engineering National Taiwan Univerity ihwang@ntu.edu.tw November 26, 213 1 / 34 王奕翔 DE Lecture 1 Solving an initial value problem aociated
More informationHybrid Projective Dislocated Synchronization of Liu Chaotic System Based on Parameters Identification
www.ccenet.org/ma Modern Applied Science Vol. 6, No. ; February Hybrid Projective Dilocated Synchronization of Liu Chaotic Sytem Baed on Parameter Identification Yanfei Chen College of Science, Guilin
More informationStochastic Optimization with Inequality Constraints Using Simultaneous Perturbations and Penalty Functions
Stochatic Optimization with Inequality Contraint Uing Simultaneou Perturbation and Penalty Function I-Jeng Wang* and Jame C. Spall** The John Hopkin Univerity Applied Phyic Laboratory 11100 John Hopkin
More informationAvoiding Forbidden Submatrices by Row Deletions
Avoiding Forbidden Submatrice by Row Deletion Sebatian Wernicke, Jochen Alber, Jen Gramm, Jiong Guo, and Rolf Niedermeier Wilhelm-Schickard-Intitut für Informatik, niverität Tübingen, Sand 13, D-72076
More informationarxiv: v1 [math.mg] 25 Aug 2011
ABSORBING ANGLES, STEINER MINIMAL TREES, AND ANTIPODALITY HORST MARTINI, KONRAD J. SWANEPOEL, AND P. OLOFF DE WET arxiv:08.5046v [math.mg] 25 Aug 20 Abtract. We give a new proof that a tar {op i : i =,...,
More informationResearch Article Reliability of Foundation Pile Based on Settlement and a Parameter Sensitivity Analysis
Mathematical Problem in Engineering Volume 2016, Article ID 1659549, 7 page http://dxdoiorg/101155/2016/1659549 Reearch Article Reliability of Foundation Pile Baed on Settlement and a Parameter Senitivity
More informationLecture 21. The Lovasz splitting-off lemma Topics in Combinatorial Optimization April 29th, 2004
18.997 Topic in Combinatorial Optimization April 29th, 2004 Lecture 21 Lecturer: Michel X. Goeman Scribe: Mohammad Mahdian 1 The Lovaz plitting-off lemma Lovaz plitting-off lemma tate the following. Theorem
More informationOptimal Strategies for Utility from Terminal Wealth with General Bid and Ask Prices
http://doi.org/10.1007/00245-018-9550-5 Optimal Strategie for Utility from Terminal Wealth with General Bid and Ak Price Tomaz Rogala 1 Lukaz Stettner 2 The Author 2018 Abtract In the paper we tudy utility
More informationResearch Article Frequent Oscillatory Behavior of Delay Partial Difference Equations with Positive and Negative Coefficients
Hindawi Publishing Corporation Advances in Difference Equations Volume 2010, Article ID 606149, 15 pages doi:10.1155/2010/606149 Research Article Frequent Oscillatory Behavior of Delay Partial Difference
More informationINITIAL-VALUE PROBLEMS FOR HYBRID HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS
Electronic Journal of Differential Equation, Vol. 204 204, No. 6, pp. 8. ISSN: 072-669. URL: http://ejde.math.txtate.edu or http://ejde.math.unt.edu ftp ejde.math.txtate.edu INITIAL-VALUE PROBLEMS FOR
More informationAsymptotic behavior of solutions of mixed problem for linear thermo-elastic systems with microtemperatures
Mathematica Aeterna, Vol. 8, 18, no. 4, 7-38 Aymptotic behavior of olution of mixed problem for linear thermo-elatic ytem with microtemperature Gulhan Kh. Shafiyeva Baku State Univerity Intitute of Mathematic
More informationResearch Article Existence of Periodic Positive Solutions for Abstract Difference Equations
Discrete Dynamics in Nature and Society Volume 2011, Article ID 870164, 7 pages doi:10.1155/2011/870164 Research Article Existence of Periodic Positive Solutions for Abstract Difference Equations Shugui
More information722 Chen Xiang-wei et al. Vol. 9 r i and _r i are repectively the poition vector and the velocity vector of the i-th particle and R i = dm i dt u i; (
Volume 9, Number 10 October, 2000 1009-1963/2000/09(10)/0721-05 CHINESE PHYSICS cfl 2000 Chin. Phy. Soc. PERTURBATION TO THE SYMMETRIES AND ADIABATIC INVARIANTS OF HOLONOMIC VARIABLE MASS SYSTEMS * Chen
More informationCharacterizations of Type-2 Harmonic Curvatures and General Helices in Euclidean space E⁴ Faik Babadag
Characterization of Type-2 Harmonic Curvature and General Helice in Euclidean pace E⁴ Faik Babadag Department of MATHEMATICS, KIRIKKALE Univerity, KIRIKKALE Email: faik.babadag@kku.edu.tr Abtract In thi
More informationA Constraint Propagation Algorithm for Determining the Stability Margin. The paper addresses the stability margin assessment for linear systems
A Contraint Propagation Algorithm for Determining the Stability Margin of Linear Parameter Circuit and Sytem Lubomir Kolev and Simona Filipova-Petrakieva Abtract The paper addree the tability margin aement
More informationModule 4: Time Response of discrete time systems Lecture Note 1
Digital Control Module 4 Lecture Module 4: ime Repone of dicrete time ytem Lecture Note ime Repone of dicrete time ytem Abolute tability i a baic requirement of all control ytem. Apart from that, good
More informationA Full-Newton Step Primal-Dual Interior Point Algorithm for Linear Complementarity Problems *
ISSN 76-7659, England, UK Journal of Information and Computing Science Vol 5, No,, pp 35-33 A Full-Newton Step Primal-Dual Interior Point Algorithm for Linear Complementarity Problem * Lipu Zhang and Yinghong
More informationOptimal financing and dividend control of the insurance company with proportional reinsurance policy
Inurance: Mathematic and Economic 42 28 976 983 www.elevier.com/locate/ime Optimal financing and dividend control of the inurance company with proportional reinurance policy Lin He a, Zongxia Liang b,
More informationNoether symmetry and non-noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations
Vol 16 No 11, November 2007 c 2007 Chin. Phy. Soc. 1009-1963/2007/1611/3182-05 Chinee Phyic and IOP Publihing Ltd Noether ymmetry and non-noether conerved quantity of the relativitic holonomic nonconervative
More informationMath 273 Solutions to Review Problems for Exam 1
Math 7 Solution to Review Problem for Exam True or Fale? Circle ONE anwer for each Hint: For effective tudy, explain why if true and give a counterexample if fale (a) T or F : If a b and b c, then a c
More informationManprit Kaur and Arun Kumar
CUBIC X-SPLINE INTERPOLATORY FUNCTIONS Manprit Kaur and Arun Kumar manpreet2410@gmail.com, arun04@rediffmail.com Department of Mathematic and Computer Science, R. D. Univerity, Jabalpur, INDIA. Abtract:
More informationSome Stability and Boundedness Conditions for Second-order Leaderless and Leader-following Consensus with Communication and Input Delays
010 American Control Conference Marriott Waterfront, Baltimore, MD, USA June 30-July 0, 010 WeA16.4 Some Stability and Boundedne Condition for Second-order Leaderle and Leader-following Conenu with Communication
More informationOn the Relationship Between Continuous- and Discrete-Time Control Systems
On the Relationhip Between Continuou- and Dicrete-Time Control Sytem V.M. Veliov Reearch Report 21-13 November, 21 Operation Reearch and Control Sytem Intitute of Mathematical Method in Economic Vienna
More informationChapter 7: The Laplace Transform
Chapter 7: The Laplace Tranform 王奕翔 Department of Electrical Engineering National Taiwan Univerity ihwang@ntu.edu.tw November 2, 213 1 / 25 王奕翔 DE Lecture 1 Solving an initial value problem aociated with
More informationDipartimento di Matematica
Dipartimento di Matematica P. Bonicatto, L. Luardi Analyi of an integral equation ariing from a variational problem Rapporto interno N. 5, luglio 29 Politecnico di Torino Coro Duca degli Abruzzi, 24-29
More informationMA 266 FINAL EXAM INSTRUCTIONS May 2, 2005
MA 66 FINAL EXAM INSTRUCTIONS May, 5 NAME INSTRUCTOR. You mut ue a # pencil on the mark ene heet anwer heet.. If the cover of your quetion booklet i GREEN, write in the TEST/QUIZ NUMBER boxe and blacken
More informationDelay-Dependent Stability Criteria for Linear Time-Delay System of Neutral Type
World Academy of Science Engineering and Technology Vol:4 No:1 1 Delay-Dependent Stability Criteria for Linear Time-Delay Sytem of Neutral Type Myeongjin Park Ohmin Kwon Juhyun Park and Sangmoon Lee International
More informationA note on the bounds of the error of Gauss Turán-type quadratures
Journal of Computational and Applied Mathematic 2 27 276 282 www.elevier.com/locate/cam A note on the bound of the error of Gau Turán-type quadrature Gradimir V. Milovanović a, Miodrag M. Spalević b, a
More informationProblem Set 8 Solutions
Deign and Analyi of Algorithm April 29, 2015 Maachuett Intitute of Technology 6.046J/18.410J Prof. Erik Demaine, Srini Devada, and Nancy Lynch Problem Set 8 Solution Problem Set 8 Solution Thi problem
More information7.2 INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES 281
72 INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES 28 and i 2 Show how Euler formula (page 33) can then be ued to deduce the reult a ( a) 2 b 2 {e at co bt} {e at in bt} b ( a) 2 b 2 5 Under what condition
More informationLaplace Transformation
Univerity of Technology Electromechanical Department Energy Branch Advance Mathematic Laplace Tranformation nd Cla Lecture 6 Page of 7 Laplace Tranformation Definition Suppoe that f(t) i a piecewie continuou
More informationA characterization of nonhomogeneous wavelet dual frames in Sobolev spaces
Zhang and Li Journal of Inequalitie and Application 016) 016:88 DOI 10.1186/13660-016-13-8 R E S E A R C H Open Acce A characterization of nonhomogeneou wavelet dual frame in Sobolev pace Jian-Ping Zhang
More informationInvariant Unstable Manifolds of Nonautonomous Systems on Time Scales
Journal of Advance in Applied Mathematic, Vol. 4, No. 2, April 2019 http://dx.doi.org/10.22606/jaam.2019.42001 37 Invariant Untable Manifold of Nonautonomou Sytem on Time Scale Le Huy Tien 1, Nguyen Minh
More informationAn Inequality for Nonnegative Matrices and the Inverse Eigenvalue Problem
An Inequality for Nonnegative Matrice and the Invere Eigenvalue Problem Robert Ream Program in Mathematical Science The Univerity of Texa at Dalla Box 83688, Richardon, Texa 7583-688 Abtract We preent
More information