A Multiplicity Theorem for Locally Lipschitz Periodic Functionals

We prove in this paper a multiplicity theorem of the Ljusternik-Schnirelmann type for locally Lipschitz periodic funcitonals and related results. The key argument in our proofs is Ekeland′s variational principle and a non-smooth pseudo-gradient lemma. As an application of these abstract results we solve a non-linear set-valued elliptic problem.