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Homoclinic solutions of discrete nonlinear systems via variational method
Keywords:discrete nonlinear systems, homoclinic orbits, 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.