By the use of a generalized version of the Poincare'–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 [14]. We thus provide a new proof of a theorem by Mawhin and Willem [26], originally obtained by the use of variational methods.

Periodic solutions of pendulum-like Hamiltonian systems in the plane

TOADER, Rodica
2012-01-01

Abstract

By the use of a generalized version of the Poincare'–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 [14]. We thus provide a new proof of a theorem by Mawhin and Willem [26], originally obtained by the use of variational methods.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/869567
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