  The classical Mountain Pass Lemma of Ambrosetti-Rabinowitz has been studied,
extended and modified in several directions. Notable examples would certainly
include the generalization to locally Lipschitz functionals by K.C. Chang,
analyzing the structure of the critical set in the mountain pass theorem in the
works of Hofer, Pucci-Serrin and Tian, and the extension by Ghoussoub-Preiss to
closed subsets in a Banach space with recent variations. In this paper, we
utilize the generalized gradient of Clarke and Ekeland's variatonal principle
to generalize the Ghoussoub-Preiss's Theorem in the setting of locally
Lipschitz functionals. We give an application to periodic solutions of
Hamiltonian systems.
