A Poincar\'e-Birkhoff theorem for multivalued successor maps with applications to periodic superlinear Hamiltonian systems
| Autor: | Feltrin, Guglielmo, Fonda, Alessandro, Sfecci, Andrea |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11784-024-01128-5 |
| Popis: | 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. Comment: 21 pages, 4 figures |
| Databáze: | arXiv |
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