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Homoclinic solutions of discrete nonlinear systems via variational method. (English) Zbl 1462.39003

Summary: 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.

MSC:

39A12 Discrete version of topics in analysis
39A23 Periodic solutions of difference equations
37C29 Homoclinic and heteroclinic orbits for dynamical systems
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