Homoclinic solutions for a higher order difference equation withp-Laplacian

We study a higher order difference equation defined on Z with p -Laplacian and containing both advance and retardation. By using the critical point theory, sufficient conditions are obtained for the existence of infinitely many homoclinic solutions of the equation. The proof is based on the fountain theorem in combination with the variational technique. In particular, considerable effort has been made in the paper to construct a variational framework for the problem under study. Some known results in the literature are extended and complemented.