We prove the existence of infinitely many subharmonic solutions, with prescribed nodal properties, for a planar Hamiltonian system $Jz' = \nabla_z H(t,z)$, with $H$ periodic in the first variable. The goal is achieved by performing estimates of the rotation numbers with respect to deformed polar coordinates and applying Ding's version of the Poincar\'{e}-Birkhoff fixed point theorem.
Subharmonic solutions of planar Hamiltonian systems: a rotation number approach
BOSCAGGIN, Alberto
2011-01-01
Abstract
We prove the existence of infinitely many subharmonic solutions, with prescribed nodal properties, for a planar Hamiltonian system $Jz' = \nabla_z H(t,z)$, with $H$ periodic in the first variable. The goal is achieved by performing estimates of the rotation numbers with respect to deformed polar coordinates and applying Ding's version of the Poincar\'{e}-Birkhoff fixed point theorem.
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