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Nonexistence of Periodic Orbits for Forced–Damped Potential Systems in Bounded Domains

  • Florian KogelbauerEmail author
Article
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Abstract

We prove \(L^r\)-estimates on periodic solutions of periodically forced, linearly damped mechanical systems with polynomially bounded potentials. The estimates are applied to obtain a nonexistence result of periodic solutions in bounded domains, depending on an upper bound on the gradient of the potential. The results are illustrated on examples.

Keywords

Nonexistence of periodic orbits Forced-damped mechanical systems \(L^p\)-estimates 

Mathematics Subject Classification

37N05 70K40 

Notes

Acknowledgements

The author would like to thank Thomas Breunung and George Haller for several useful comments and suggestions. The author would like to thank the anonymous reviewers for their helpful comments and suggestions.

Funding

No funding has been receive.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Institute for Mechanical SystemsETH ZürichZurichSwitzerland

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