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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

Δ 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:
39A12Discrete version of topics in analysis
39A30Stability theory (difference equations)
37C29Homoclinic and heteroclinic orbits
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