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

Ribarska, Nadezhda; Tsachev, Tsvetomir; Krastanov, Mikhail

Serdica Mathematical Journal (1995)

- Volume: 21, Issue: 3, page 239-266
- ISSN: 1310-6600

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topRibarska, Nadezhda, Tsachev, Tsvetomir, and Krastanov, Mikhail. "Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds." Serdica Mathematical Journal 21.3 (1995): 239-266. <http://eudml.org/doc/11670>.

@article{Ribarska1995,

abstract = {∗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.},

author = {Ribarska, Nadezhda, Tsachev, Tsvetomir, Krastanov, Mikhail},

journal = {Serdica Mathematical Journal},

keywords = {Deformation Lemma; Ljusternik-Schnirelmann Theory; Mountain Pass Theorem; C1–Finsler Manifold; Locally Lipschitz Functions; minimax theorem; -Finsler manifold; locally Lipschitz function; deformation lemma; theorem of Lyusternik-Schnirelman; mountain pass theorem},

language = {eng},

number = {3},

pages = {239-266},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds},

url = {http://eudml.org/doc/11670},

volume = {21},

year = {1995},

}

TY - JOUR

AU - Ribarska, Nadezhda

AU - Tsachev, Tsvetomir

AU - Krastanov, Mikhail

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

JO - Serdica Mathematical Journal

PY - 1995

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 21

IS - 3

SP - 239

EP - 266

AB - ∗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.

LA - eng

KW - Deformation Lemma; Ljusternik-Schnirelmann Theory; Mountain Pass Theorem; C1–Finsler Manifold; Locally Lipschitz Functions; minimax theorem; -Finsler manifold; locally Lipschitz function; deformation lemma; theorem of Lyusternik-Schnirelman; mountain pass theorem

UR - http://eudml.org/doc/11670

ER -

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