Second order nonautonomous systems with symmetric potential changing sign
In this paper we deal with the problem of multiplicity of periodic solutions for a class of nonautonomous second order Hamiltonian systems, having indefinite potential. In the particular case that the quadratic part of the potential is negative definite, one reaches a result of subharmonic and homoc...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
1998-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1998(2)/367-379.pdf |
| _version_ | 1817968224464011264 |
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| author | F. Antonacci P. Magrone |
| author_facet | F. Antonacci P. Magrone |
| author_sort | F. Antonacci |
| collection | DOAJ |
| description | In this paper we deal with the problem of multiplicity of periodic solutions for a class of nonautonomous second order Hamiltonian systems, having indefinite potential. In the particular case that the quadratic part of the potential is negative definite, one reaches a result of subharmonic and homoclinic solutions. The proof of the multiplicity results is based on the Ljusternik-Schnirelmam category theory; the subharmonic solutions are obtained through the constrained minima of the functional to a suitable manifold, and the homoclinics are obtained with a limit procedure starting by the sequence of subharmonics. |
| first_indexed | 2024-04-13T20:05:03Z |
| format | Article |
| id | doaj.art-93d78bc7af2e42af83b68fe47a441e8c |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-04-13T20:05:03Z |
| publishDate | 1998-01-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-93d78bc7af2e42af83b68fe47a441e8c2022-12-22T02:32:01ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33501998-01-01182367379Second order nonautonomous systems with symmetric potential changing signF. Antonacci0 P. Magrone1Università di Roma TreUniversità di Roma TreIn this paper we deal with the problem of multiplicity of periodic solutions for a class of nonautonomous second order Hamiltonian systems, having indefinite potential. In the particular case that the quadratic part of the potential is negative definite, one reaches a result of subharmonic and homoclinic solutions. The proof of the multiplicity results is based on the Ljusternik-Schnirelmam category theory; the subharmonic solutions are obtained through the constrained minima of the functional to a suitable manifold, and the homoclinics are obtained with a limit procedure starting by the sequence of subharmonics.https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1998(2)/367-379.pdfhamiltonian systemsperiodic solutionssubharmonics |
| spellingShingle | F. Antonacci P. Magrone Second order nonautonomous systems with symmetric potential changing sign Rendiconti di Matematica e delle Sue Applicazioni hamiltonian systems periodic solutions subharmonics |
| title | Second order nonautonomous systems with symmetric potential changing sign |
| title_full | Second order nonautonomous systems with symmetric potential changing sign |
| title_fullStr | Second order nonautonomous systems with symmetric potential changing sign |
| title_full_unstemmed | Second order nonautonomous systems with symmetric potential changing sign |
| title_short | Second order nonautonomous systems with symmetric potential changing sign |
| title_sort | second order nonautonomous systems with symmetric potential changing sign |
| topic | hamiltonian systems periodic solutions subharmonics |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1998(2)/367-379.pdf |
| work_keys_str_mv | AT fantonacci secondordernonautonomoussystemswithsymmetricpotentialchangingsign AT pmagrone secondordernonautonomoussystemswithsymmetricpotentialchangingsign |