Abstract and Applied Analysis
Volume 7 (2002), Issue 3, Pages 143-154

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

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.


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.