A Poincaré-Birkhoff theorem for multivalued successor maps with applications to periodic superlinear Hamiltonian systems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913565824253952 |
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| author | Feltrin, Guglielmo Fonda, Alessandro Sfecci, Andrea |
| author_facet | Feltrin, Guglielmo Fonda, Alessandro Sfecci, Andrea |
| contents | 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 $\ddot x + λg(t,x) = 0$, for $λ>0$ sufficiently small, with $g(t,x)$ having a superlinear growth at infinity, without requiring the existence of an equilibrium point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21045 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Poincaré-Birkhoff theorem for multivalued successor maps with applications to periodic superlinear Hamiltonian systems Feltrin, Guglielmo Fonda, Alessandro Sfecci, Andrea Classical Analysis and ODEs 34B08, 34C25, 37J46 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 $\ddot x + λg(t,x) = 0$, for $λ>0$ sufficiently small, with $g(t,x)$ having a superlinear growth at infinity, without requiring the existence of an equilibrium point. |
| title | A Poincaré-Birkhoff theorem for multivalued successor maps with applications to periodic superlinear Hamiltonian systems |
| topic | Classical Analysis and ODEs 34B08, 34C25, 37J46 |
| url | https://arxiv.org/abs/2410.21045 |