  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 in K.C. Chang,
analysis of the structure of the critical set in the mountain pass theorem by
Hofer and Pucci-Serrin and Tian, the extension by Ghoussoub-Preiss to closed
subsets in a Banach space, and variations found in the recent Peral . In this
paper, we utilize the generalized gradient of Clarke and Ekeland's variational
principle to generalize the Ghoussoub-Preiss's Theorem in the setting of
locally Lipschitz functionals.
