Existence of two periodic solutions to general anisotropic Euler-Lagrange equations

Abstract

This paper is concerned with the following Euler-Lagrange systemwhere Lagrangian is given by L = F (t, x, v) + V (t, x) + f (t), x , growth conditions are determined by an anisotropic G-function and some geometric conditions at infinity. We consider two cases: with and without forcing term f . Using a general version of the Mountain Pass Theorem and Ekeland's variational principle we prove the existence of at least two nontrivial periodic solutions in an anisotropic Orlicz-Sobolev space.2010 Mathematics Subject Classification. 46E30 , 46E40.