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Multiple solutions of discrete Schrödinger equations with growing potentials. (English) Zbl 1419.35171

Summary: Under some weaker conditions than elsewhere, we obtain infinitely many homoclinic solutions for a class of discrete Schrödinger equations in infinite \(m\) dimensional lattices with nonlinearities being superlinear at infinity by using variational methods. Our result extends some existing results in the literature.

MSC:

35Q51 Soliton equations
35Q55 NLS equations (nonlinear Schrödinger equations)
39A12 Discrete version of topics in analysis
39A70 Difference operators
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