Existence of infinitely many homoclinic orbits for fourth-order difference systems containing both advance and retardation

Abstract By using the symmetric mountain pass theorem, we establish some existence criteria to guarantee the fourth-order difference system Δ4u(n − 2) + q(n)u(n) = f(n, u(n + 1), u(n), u(n − 1)) have infinitely many homoclinic orbits, where n ∈ Z , u ∈ R N , q : Z → R N × N and f : Z × R 3 N → R are no periodic in n.

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