Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 1, pp. 47-59 (2004)

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Critical point theorems on Finsler manifolds

László Kozma, Alexandru Kristály and Csaba Varga

Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary, e-mail:; Faculty of Mathematics and Informatics, Babes-Bolyai University Str. Kogalniceanu nr.1, R-3400 Cluj--Napoca, Romania, e-mail:

Abstract: In this paper we consider a dominating Finsler metric on a complete Riemannian manifold. First we prove that the energy integral of the Finsler metric satisfies the Palais-Smale condition, and ask for the number of geodesics with endpoints in two given submanifolds. Using Lusternik-Schnirelman theory of critical points we obtain some multiplicity results for the number of Finsler-geodesics between two submanifolds.

Keywords: Finsler manifold, critical point theory, Palais-Smale condition, Lusternik-Schnirelman theory.

Classification (MSC2000): 53C60, 58B20; 58E05

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Electronic version published on: 5 Mar 2004. This page was last modified: 4 May 2006.

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