HOMOCLINIC SOLUTIONS OF DISCRETE NONLINEAR SYSTEMS VIA VARIATIONAL METHOD

Lynn Erbe; Baoguo Jia; Qinqin Zhang

doi:10.11948/2019.271

2019 Volume 9 Issue 1

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Lynn Erbe, Baoguo Jia, Qinqin Zhang. HOMOCLINIC SOLUTIONS OF DISCRETE NONLINEAR SYSTEMS VIA VARIATIONAL METHOD[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 271-294. doi: 10.11948/2019.271

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Lynn Erbe, Baoguo Jia, Qinqin Zhang. HOMOCLINIC SOLUTIONS OF DISCRETE NONLINEAR SYSTEMS VIA VARIATIONAL METHOD[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 271-294. doi: 10.11948/2019.271

HOMOCLINIC SOLUTIONS OF DISCRETE NONLINEAR SYSTEMS VIA VARIATIONAL METHOD

1.
Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE, 68588-0130, USA
2.
School Of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, China
3.
Guangdong Province Key Laboratory of Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China
4.
Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, China

Corresponding author: Email address:qqzhang@gzhu.edu.cn(Q. Zhang)
Fund Project: The authors were supported by National Natural Science Foundation of China (11471085, 11271380) and Guangdong Province Key Laboratory of Computational Science

Abstract

Abstract

Homoclinic solutions arise in various discrete models with variational structure, from discrete nonlinear Schrödinger equations to discrete Hamiltonian systems. In recent years, a lot of interesting results on the homoclinic solutions of difference equations have been obtained. In this paper, we review some recent progress by using critical point theory to study the existence and multiplicity results of homoclinic solutions in some discrete nonlinear systems with variational structure.
- Discrete nonlinear system /
- homoclinic solutions /
- variational method
MSC: 39A12, 39A23

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References

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