Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-Laplacian

被引：4

作者：

Zhang, Qiongfen ^{[1
]}

Tang, X. H. ^{[1
]}

机构：

[1] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410083, Hunan, Peoples R China

来源：

ABSTRACT AND APPLIED ANALYSIS | 2011年

关键词：

2ND-ORDER HAMILTONIAN-SYSTEMS; PERIODIC-SOLUTIONS; SUBHARMONIC SOLUTIONS; EQUATIONS; RETARDATION; ADVANCE;

D O I：

10.1155/2011/351562

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By applying a variant version of Mountain Pass Theorem in critical point theory, we prove the existence of homoclinic solutions for the following asymptotically p-linear difference system with p-Laplacian Delta(vertical bar Delta u(n - 1)vertical bar(p-2)Delta u(n - 1)) +del[-K(n, u(n)) + W(n, u(n))] = 0, where p is an element of (1, +infinity), n is an element of Z, u is an element of R(N), K, W : Z x R(N) -> R are not periodic in n, andWis asymptotically p-linear at infinity.

引用

页数：17

共 30 条

[1]

Agarwal R.P., 2000, MONOGRAPHS TXB PURE, V228

[2] Multiple positive solutions of singular discrete p-Laplacian problems via variational methods [J].

Agarwal, Ravi P. ;

Perera, Kanishka ;

O'Regan, Donal .

ADVANCES IN DIFFERENCE EQUATIONS, 2005, 2005 (02) :93-99

[3] PERIODIC-SOLUTIONS OF FIRST-ORDER LINEAR DIFFERENCE-EQUATIONS [J].

AGARWAL, RP ;

POPENDA, J .

MATHEMATICAL AND COMPUTER MODELLING, 1995, 22 (01) :11-19

[4]

Ahlbrandt C. D., 1996, KLUWER TEXTS MATH SC, V16

[5]

[Anonymous], 1979, Istit. Lombardo Accad. Sci. Lett. Rend. A

[6]

[Anonymous], 1899, Les Methods Nouvells de la Mecanique Leleste

[7] Existence of homoclinic orbits for 2nth-order nonlinear difference equations containing both many advances and retardations [J].

Chen, Peng ;

Tang, Xianhua .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 381 (02) :485-505

[8] Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations [J].

Chen, Peng ;

Tang, X. H. .

ADVANCES IN DIFFERENCE EQUATIONS, 2010,

[9] Existence of infinitely many homoclinic orbits for fourth-order difference systems containing both advance and retardation [J].

Chen, Peng ;

Tang, X. H. .

APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (09) :4408-4415

[10]

Elaydi S, 1999, UNDERGRADUATE TEXTS

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