Generic uniqueness of a minimal solution for variational problems on a torus. (English) Zbl 1001.49001

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


49J10 Existence theories for free problems in two or more independent variables
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
49J45 Methods involving semicontinuity and convergence; relaxation
Full Text: DOI EuDML