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Zbl 1207.39006
Chen, Peng; Xiao, Li
Existence of homoclinic orbit for second-order nonlinear difference equation. (English)
[J] Electron. J. Qual. Theory Differ. Equ. 2010, Paper No. 72, 14 p., electronic only (2010). ISSN 1417-3875/e

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 $t\in \Bbb Z,\ u\in \Bbb R$.

MSC 2000:: *39A12 Discrete version of topics in analysis
37C29 Homoclinic and heteroclinic orbits

Keywords: nonlinear difference equation; discrete variational methods; mountain pass Lemma; homoclinic orbit

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