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Homoclinic orbits for second order self-adjoint difference equations. (English) Zbl 1107.39022
The authors use variational methods to study the existence of nontrivial homoclinic orbits for a nonlinear difference equation. Such solutions were first discovered by Poincaré in 1899. They are also called doubly asymptotic solutions. The proof of the main result in this paper is based on the mountain pass theorem.

MSC:
39A12 Discrete version of topics in analysis
39A11 Stability of difference equations (MSC2000)
37C29 Homoclinic and heteroclinic orbits for dynamical systems
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