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Existence of infinitely many homoclinic orbits for fourth-order difference systems containing both advance and retardation. (English) Zbl 1211.39004
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.

MSC:
39A12 Discrete version of topics in analysis
39A30 Stability theory for difference equations
37C29 Homoclinic and heteroclinic orbits for dynamical systems
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