Chen, Peng; Xiao, Li Existence of homoclinic orbit for second-order nonlinear difference equation. (English) Zbl 1207.39006 Electron. J. Qual. Theory Differ. Equ. 2010, Paper No. 72, 14 p. (2010). 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 \(t\in \mathbb Z,\;u\in \mathbb R\). Cited in 3 Documents MSC: 39A12 Discrete version of topics in analysis 37C29 Homoclinic and heteroclinic orbits for dynamical systems Keywords:nonlinear difference equation; discrete variational methods; mountain pass Lemma; homoclinic orbit PDFBibTeX XMLCite \textit{P. Chen} and \textit{L. Xiao}, Electron. J. Qual. Theory Differ. Equ. 2010, Paper No. 72, 14 p. (2010; Zbl 1207.39006) Full Text: DOI EuDML EMIS