Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth
We prove the existence and multiplicity of subharmonic solutions for Hamiltonian systems obtained as perturbations of N planar uncoupled systems which, e.g., model some type of asymmetric oscillators. The nonlinearities are assumed to satisfy Landesman–Lazer conditions at the zero eigenvalue, and to...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2017-07-01
|
| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2017-0040 |
| _version_ | 1818715948135219200 |
|---|---|
| author | Fonda Alessandro Toader Rodica |
| author_facet | Fonda Alessandro Toader Rodica |
| author_sort | Fonda Alessandro |
| collection | DOAJ |
| description | We prove the existence and multiplicity of subharmonic solutions for Hamiltonian systems obtained as perturbations of N planar uncoupled systems which, e.g., model some type of asymmetric oscillators. The nonlinearities are assumed to satisfy Landesman–Lazer conditions at the zero eigenvalue, and to have some kind of sublinear behavior at infinity. The proof is carried out by the use of a generalized version of the Poincaré–Birkhoff Theorem. Different situations, including Lotka–Volterra systems, or systems with singularities, are also illustrated. |
| first_indexed | 2024-12-17T19:11:28Z |
| format | Article |
| id | doaj.art-e3a5d28f2e9248fe82785038328e5edd |
| institution | Directory Open Access Journal |
| issn | 2191-9496 2191-950X |
| language | English |
| last_indexed | 2024-12-17T19:11:28Z |
| publishDate | 2017-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-e3a5d28f2e9248fe82785038328e5edd2022-12-21T21:35:52ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2017-07-018158360210.1515/anona-2017-0040anona-2017-0040Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growthFonda Alessandro0Toader Rodica1Dipartimento di Matematica e Geoscienze, Università di Trieste, P.le Europa 1, 34127Trieste, ItalyDipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, Via delle Scienze 206, 33100Udine, ItalyWe prove the existence and multiplicity of subharmonic solutions for Hamiltonian systems obtained as perturbations of N planar uncoupled systems which, e.g., model some type of asymmetric oscillators. The nonlinearities are assumed to satisfy Landesman–Lazer conditions at the zero eigenvalue, and to have some kind of sublinear behavior at infinity. The proof is carried out by the use of a generalized version of the Poincaré–Birkhoff Theorem. Different situations, including Lotka–Volterra systems, or systems with singularities, are also illustrated.https://doi.org/10.1515/anona-2017-0040hamiltonian systemssubharmonic solutionspoincaré–birkhofflotka–volterra34c25 |
| spellingShingle | Fonda Alessandro Toader Rodica Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth Advances in Nonlinear Analysis hamiltonian systems subharmonic solutions poincaré–birkhoff lotka–volterra 34c25 |
| title | Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth |
| title_full | Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth |
| title_fullStr | Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth |
| title_full_unstemmed | Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth |
| title_short | Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth |
| title_sort | subharmonic solutions of hamiltonian systems displaying some kind of sublinear growth |
| topic | hamiltonian systems subharmonic solutions poincaré–birkhoff lotka–volterra 34c25 |
| url | https://doi.org/10.1515/anona-2017-0040 |
| work_keys_str_mv | AT fondaalessandro subharmonicsolutionsofhamiltoniansystemsdisplayingsomekindofsublineargrowth AT toaderrodica subharmonicsolutionsofhamiltoniansystemsdisplayingsomekindofsublineargrowth |