Abstract and Applied Analysis

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Abstract and Applied Analysis / 2002 / Article

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Volume 7 |Article ID 460976 | 12 pages | https://doi.org/10.1155/S1085337502000842

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

Alexander J. Zaslavski1

1Department of Mathematics, Technion-Israel Institute of Technology, Israel

Received17 Jul 2001

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.

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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