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

Ribarska, 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 -