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
Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel
Received 17 July 2001
Copyright © 2002 Alexander J. Zaslavski. 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.
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.