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Volume 21 Number 3 >

Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/641

Title: Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds
Authors: Ribarska, Nadezhda
Tsachev, Tsvetomir
Krastanov, Mikhail
Keywords: Deformation Lemma
Ljusternik-Schnirelmann Theory
Mountain Pass Theorem
C1–Finsler Manifold
Locally Lipschitz Functions
Issue Date: 1995
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 21, No 3, (1995), 239p-266p
Abstract: 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.
Description: ∗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.
URI: http://hdl.handle.net/10525/641
ISSN: 1310-6600
Appears in Collections:Volume 21 Number 3

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