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

Abstract

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 ${\Delta }_2\cap {\nabla }_2$ in infinity and globally. We give conditions on the growth of the potential near zero for both situations.