Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 21, No 3, (1995), 239p-266p
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.
∗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.