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T-Periodic solutions of time dependent Hamiltonian systems with a potential vanishing at infinity

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Abstract

We are discussing existence and multiplicity of T-periodic solutions of the time dependent Hamiltonian system\( - \ddot x\)= ∇U(x, t) under the assumption that U(x, t) approaches 0 for large |x| meaning that the force ∇U is concentrated in a finite region. Our method is variational and it is shown how the difficulties with the Palais-Smale condition can be overcome in this case.

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  1. Abteilung für Mathematik der Ruhr-Universität Bochum, Universitätsstraße 150, D-4630, Bochum

    Klaus Thews

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  1. Klaus Thews
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Thews, K. T-Periodic solutions of time dependent Hamiltonian systems with a potential vanishing at infinity. Manuscripta Math 33, 327–338 (1981). https://doi.org/10.1007/BF01798231

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  • DOI: https://doi.org/10.1007/BF01798231

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