Existence of Two Periodic Solutions to General Anisotropic Euler-Lagrange Equations

Abstract

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.