Periodic solutions of second order Hamiltonian systems with nonlinearity of general linear growth
In this paper we consider a class of second order Hamiltonian system with the nonlinearity of linear growth. Compared with the existing results, we do not assume an asymptotic of the nonlinearity at infinity to exist. Moreover, we allow the system to be resonant at zero. Under some general conditio...
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| Format: | Article |
| Language: | English |
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University of Szeged
2021-04-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8820 |
| _version_ | 1797830418676842496 |
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| author | Guanggang Liu |
| author_facet | Guanggang Liu |
| author_sort | Guanggang Liu |
| collection | DOAJ |
| description | In this paper we consider a class of second order Hamiltonian system with the nonlinearity of linear growth. Compared with the existing results, we do not assume an asymptotic of the nonlinearity at infinity to exist. Moreover, we allow the system to be resonant at zero. Under some general conditions, we will establish the existence and multiplicity of nontrivial periodic solutions by using the Morse theory and two critical point theorems. |
| first_indexed | 2024-04-09T13:36:54Z |
| format | Article |
| id | doaj.art-1399eb33cdce4373b6df4fc479c76490 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:36:54Z |
| publishDate | 2021-04-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-1399eb33cdce4373b6df4fc479c764902023-05-09T07:53:11ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752021-04-0120212711910.14232/ejqtde.2021.1.278820Periodic solutions of second order Hamiltonian systems with nonlinearity of general linear growthGuanggang Liu0School of Mathematical Sciences, Liaocheng University, Liaocheng, P.R. ChinaIn this paper we consider a class of second order Hamiltonian system with the nonlinearity of linear growth. Compared with the existing results, we do not assume an asymptotic of the nonlinearity at infinity to exist. Moreover, we allow the system to be resonant at zero. Under some general conditions, we will establish the existence and multiplicity of nontrivial periodic solutions by using the Morse theory and two critical point theorems.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8820second order hamiltonian systemsperiodic solutionsmorse theorycritical groups |
| spellingShingle | Guanggang Liu Periodic solutions of second order Hamiltonian systems with nonlinearity of general linear growth Electronic Journal of Qualitative Theory of Differential Equations second order hamiltonian systems periodic solutions morse theory critical groups |
| title | Periodic solutions of second order Hamiltonian systems with nonlinearity of general linear growth |
| title_full | Periodic solutions of second order Hamiltonian systems with nonlinearity of general linear growth |
| title_fullStr | Periodic solutions of second order Hamiltonian systems with nonlinearity of general linear growth |
| title_full_unstemmed | Periodic solutions of second order Hamiltonian systems with nonlinearity of general linear growth |
| title_short | Periodic solutions of second order Hamiltonian systems with nonlinearity of general linear growth |
| title_sort | periodic solutions of second order hamiltonian systems with nonlinearity of general linear growth |
| topic | second order hamiltonian systems periodic solutions morse theory critical groups |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8820 |
| work_keys_str_mv | AT guanggangliu periodicsolutionsofsecondorderhamiltoniansystemswithnonlinearityofgenerallineargrowth |