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Zbl 1211.39004
Chen, Peng; Tang, X.H.
Existence of infinitely many homoclinic orbits for fourth-order difference systems containing both advance and retardation. (English)
[J] Appl. Math. Comput. 217, No. 9, 4408-4415 (2011). ISSN 0096-3003

Sufficient conditions which guarantee that the fourth-order difference system of the form $$\Delta^4 u(n-2)+q(n)u(n)=f(n,u(n+1),u(n),u(n-1))$$ has infinitely many homoclinic orbits are established. Two examples illustrating the results are given.
[Ioannis P. Stavroulakis (Ioannina)]

MSC 2000:: *39A12 Discrete version of topics in analysis
39A30
37C29 Homoclinic and heteroclinic orbits

Keywords: fourth-order difference system; symmetric mountain pass theorem; homoclinic orbits

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