Stefan Suhr, Kai Zehmisch
Published 2013-05-13, updated 2015-12-18Version 2
We show that the Lagrangian of classical mechanics on a Riemannian manifold of bounded geometry carries a periodic solution of motion with rescribed energy, provided the potential satisfies an asymptotic growth condition, changes sign, and the negative set of the potential is non-trivial in the relative homology.
Comments: We weakened the assumption to be of bounded geometry
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An averaging result for periodic solutions of Carathéodory differential equations
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