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¨+λg(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
Fonda A.Secondo
;Sfecci A.Ultimo
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¨+λg(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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