Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds

∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria. ∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.

Let M be a complete C1−Finsler manifold without boundary and f : M → R be a locally Lipschitz function. The classical proof of the well known deformation lemma can not be extended in this case because integral lines may not exist. In this paper we establish existence of deformations generalizing the classical result. This allows us to prove some known results in a more general setting (minimax theorem, a theorem of Ljusternik-Schnirelmann type, mountain pass theorem). This approach enables us to drop the compactness assumptions characteristic for recent papers in the field using the Ekeland’s variational principle as the main tool.