Periodic solutions of Euler-Lagrange equations in an anisotropic Orlicz-Sobolev space setting

Abstract

We consider the problem of finding periodic solutions of certain Euler-Lagrange equations which include, among others, equations involving the p-Laplace operator and, more generally, the pp, qq-Laplace operator. We employ the direct method of the calculus of variations in the framework of anisotropic Orlicz-Sobolev spaces. These spaces appear to be useful in formulating a unified theory of existence of solutions for such a problem.