We provide a new version of the Poincaré-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 x'' + λ g(t,x) = 0, for λ>0 sufficiently small, with g(t,x) having a superlinear growth at infinity, without requiring the existence of an equilibrium point.
A Poincaré-Birkhoff theorem for multivalued successor maps with applications to periodic superlinear Hamiltonian systems
Feltrin, Guglielmo
;Sfecci, Andrea
2024-01-01
Abstract
We provide a new version of the Poincaré-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 x'' + λ g(t,x) = 0, for λ>0 sufficiently small, with g(t,x) having a superlinear growth at infinity, without requiring the existence of an equilibrium point.File in questo prodotto:
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