Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations
نویسندگان
چکیده
By using the critical point theory, we establish some existence criteria to guarantee that the nonlinear difference equation ΔΔpnΔxn − 1 δ − qnxn δ fn, xn has at least one homoclinic solution, where n ∈ Z, xn ∈ R, and f : Z × R → R is non periodic in n. Our conditions on the nonlinear term fn, xn are rather relaxed, and we generalize some existing results in the literature.
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