Homoclinic orbits for second order $$p$$ p -Laplacian difference equations containing both advance and retardation

Abstract

Using the critical point theory, we obtain the existence of a nontrivial homoclinic orbit for second order \(p\)-Laplacian difference equations containing both advance and retardation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. One of our results generalizes and improves the results in the literature.