On the existence of periodic solutions to second order Hamiltonian systems
In this paper, the existence of periodic solutions to the second order Hamiltonian systems is investigated. By introducing a new growth condition which generalizes the Ambrosetti–Rabinowitz condition, we prove a existence result of nontrivial $T$-periodic solution via the variational methods. Our re...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2022-07-01
|
| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9889 |
| _version_ | 1797830479627419648 |
|---|---|
| author | Xiao-Feng Ke Jia-Feng Liao |
| author_facet | Xiao-Feng Ke Jia-Feng Liao |
| author_sort | Xiao-Feng Ke |
| collection | DOAJ |
| description | In this paper, the existence of periodic solutions to the second order Hamiltonian systems is investigated. By introducing a new growth condition which generalizes the Ambrosetti–Rabinowitz condition, we prove a existence result of nontrivial $T$-periodic solution via the variational methods. Our result is new because it can deal with not only the superquadratic case, but also the anisotropic case which allows the potential to be superquadratic growth in only one direction and asymptotically quadratic growth in other directions. |
| first_indexed | 2024-04-09T13:36:46Z |
| format | Article |
| id | doaj.art-f7a8c49969364a39b18c9306e5d25514 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:36:46Z |
| publishDate | 2022-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-f7a8c49969364a39b18c9306e5d255142023-05-09T07:53:12ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752022-07-0120223611210.14232/ejqtde.2022.1.369889On the existence of periodic solutions to second order Hamiltonian systemsXiao-Feng Ke0Jia-Feng Liao1School of Mathematics and Statistics, Southwest University, Chongqing, P.R. ChinaSchool of Mathematics and Information, China West Normal University, Nanchong, P.R. ChinaIn this paper, the existence of periodic solutions to the second order Hamiltonian systems is investigated. By introducing a new growth condition which generalizes the Ambrosetti–Rabinowitz condition, we prove a existence result of nontrivial $T$-periodic solution via the variational methods. Our result is new because it can deal with not only the superquadratic case, but also the anisotropic case which allows the potential to be superquadratic growth in only one direction and asymptotically quadratic growth in other directions.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9889second order hamiltonian systemsperiodic solutionsexistencevariational method |
| spellingShingle | Xiao-Feng Ke Jia-Feng Liao On the existence of periodic solutions to second order Hamiltonian systems Electronic Journal of Qualitative Theory of Differential Equations second order hamiltonian systems periodic solutions existence variational method |
| title | On the existence of periodic solutions to second order Hamiltonian systems |
| title_full | On the existence of periodic solutions to second order Hamiltonian systems |
| title_fullStr | On the existence of periodic solutions to second order Hamiltonian systems |
| title_full_unstemmed | On the existence of periodic solutions to second order Hamiltonian systems |
| title_short | On the existence of periodic solutions to second order Hamiltonian systems |
| title_sort | on the existence of periodic solutions to second order hamiltonian systems |
| topic | second order hamiltonian systems periodic solutions existence variational method |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9889 |
| work_keys_str_mv | AT xiaofengke ontheexistenceofperiodicsolutionstosecondorderhamiltoniansystems AT jiafengliao ontheexistenceofperiodicsolutionstosecondorderhamiltoniansystems |