Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 1, pp. 47-59 (2004)
Critical point theorems on Finsler manifolds
László Kozma, Alexandru Kristály and Csaba VargaInstitute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary, e-mail: firstname.lastname@example.org; Faculty of Mathematics and Informatics, Babes-Bolyai University Str. Kogalniceanu nr.1, R-3400 Cluj--Napoca, Romania, e-mail: email@example.com
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.