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Existence of homoclinic orbit for second-order nonlinear difference equation. (English) Zbl 1207.39006

Summary: By using the mountain pass theorem, we establish some existence criteria to guarantee the second-order nonlinear difference equation \(\Delta \left[p(t)\Delta u(t-1)\right] +f(t,u(t))=0\) has at least one homoclinic orbit, where \(t\in \mathbb Z,\;u\in \mathbb R\).

MSC:

39A12 Discrete version of topics in analysis
37C29 Homoclinic and heteroclinic orbits for dynamical systems
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