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Advanced Nonlinear Studies

Editor-in-Chief: Ahmad, Shair

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Volume 12, Issue 2


Periodic Solutions of Pendulum-Like Hamiltonian Systems in the Plane

Alessandro Fonda / Rodica Toader
Published Online: 2016-03-10 | DOI: https://doi.org/10.1515/ans-2012-0210


By the use of a generalized version of the Poincaré-Birkhoff fixed point theorem, we prove the existence of at least two periodic solutions for a class of Hamiltonian systems in the plane, having in mind the forced pendulum equation as a particular case. Our approach is closely related to the one used by Franks in [15], but the proof remains at a more elementary level.

Keywords : Pendulum equation; Poincaré-Birkhoff theorem; nonlinear dynamics

About the article

Published Online: 2016-03-10

Published in Print: 2012-05-01

Citation Information: Advanced Nonlinear Studies, Volume 12, Issue 2, Pages 395–408, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2012-0210.

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© 2016 by Advanced Nonlinear Studies, Inc..

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