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Homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity. (English) Zbl 1284.39006

The existence of homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity is considered. The classical Ambrosetti-Rabinowitz superlinear condition is improved by a general superlinear one. The main idea in this paper is an application of a linking theorem combined with an approximation technique.

MSC:

39A10 Additive difference equations
39A70 Difference operators
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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