Periodic Solutions of Euler–Lagrange Equations in an Anisotropic Orlicz–Sobolev Space Setting

In this paper we consider the problem of finding periodic solutions of certain Euler-Lagrange equations, which include, among others, equations involving the p-Laplace and, more generality, the (p,q)-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 for the type of problem considered.