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Volume 9, Number 1, 2019, Pages 271-294                                                                DOI:10.11948/2019.271
Homoclinic solutions of discrete nonlinear systems via variational method
Lynn Erbe,Baoguo Jia,Qinqin Zhang
Keywords:Discrete nonlinear system, homoclinic solutions, variational method.
Abstract:
      Homoclinic solutions arise in various discrete models with variational structure, from discrete nonlinear Schr\"{o}dinger 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.
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