Homoclinic solutions for a class of nonlinear fourth order [formula omitted]-Laplacian differential equations

Abstract

The aim of this paper is the study of existence of homoclinic solutions for a class of nonlinear differential equations involving p-Laplacian. Under suitable growth conditions we prove that the considered problem has at least one nontrivial homoclinic solution. The proof is based on the mountain-pass theorem with Cerami’s condition, Brezis–Lieb lemma and variational method.