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Abstract
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Abstract and Applied Analysis
Volume 7 (2002), Issue 3, Pages 143-154
doi:10.1155/S1085337502000842

Generic uniqueness of a minimal solution for variational problems on a torus

Alexander J. Zaslavski

Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel

Abstract

We study minimal solutions for one-dimensional variational problems on a torus. We show that, for a generic integrand and any rational number α, there exists a unique (up to translations) periodic minimal solution with rotation number α.