Mountain pass type periodic solutions for Euler-Lagrange equations in anisotropic Orlicz-Sobolev space

摘要

Using the Mountain Pass Theorem, we establish the existence of periodic solution for Euler-Lagrange equation. Lagrangian consists of kinetic part (an anisotropic G-function), potential part K - W and a forcing term. We consider two situations: G satisfying Delta(2) boolean AND del 2 at infinity and globally. We give conditions on the growth of the potential near zero for both situations. (C) 2018 Elsevier Inc. All rights reserved.