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.File in questo prodotto:
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