Periodic perturbations of Hamiltonian systems

We prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincaré–Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second par...

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Bibliographic Details
Published in:Advances in nonlinear analysis 2016-11, Vol.5 (4), p.367-382
Main Authors: Fonda, Alessandro, Garrione, Maurizio, Gidoni, Paolo
Format: Article
Language:English
Subjects:
34C25
47H15
Periodic solutions
perturbation theory
Poincaré–Birkhoff theorem
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Summary:We prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincaré–Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second part we focus on some suitable global conditions, so to deal with weakly coupled systems.
ISSN:2191-9496
2191-950X
DOI:10.1515/anona-2015-0122