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arXiv · 2410.21045

A Poincar\'e-Birkhoff theorem for multivalued successor maps with applications to periodic superlinear Hamiltonian systems

Guglielmo Feltrin·Alessandro Fonda·Andrea Sfecci
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Abstract

We provide a new version of the Poincar\'e-Birkhoff theorem for possibly multivalued successor maps associated with planar non-autonomous Hamiltonian systems. As an application, we prove the existence of periodic and subharmonic solutions of the scalar second order equation $\ddot x + \lambda g(t,x) = 0$, for $\lambda>0$ sufficiently small, with $g(t,x)$ having a superlinear growth at infinity, without requiring the existence of an equilibrium point.

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Guglielmo Feltrin, Alessandro Fonda, Andrea Sfecci. 2024-10-28. A Poincar\'e-Birkhoff theorem for multivalued successor maps with applications to periodic superlinear Hamiltonian systems. https://doi.org/10.1007/s11784-024-01128-5

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