The minimal periodic solutions for superquadratic autonomous Hamiltonian systems without the Palais-Smale condition
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914626176811008 |
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| author | Xiao, Yuming Zhu, Gaosheng |
| author_facet | Xiao, Yuming Zhu, Gaosheng |
| contents | In this paper, we prove the existence of periodic solutions with any prescribed minimal period $T>0$ for even second order Hamiltonian systems and convex first order Hamiltonian systems under the weak Nehari condition instead of Ambrosetti-Rabinowitz's. To this end, we shall develop the method of Nehari manifold to directly deal with a frequently occurring problem where the Nehari manifold is not a manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00655 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The minimal periodic solutions for superquadratic autonomous Hamiltonian systems without the Palais-Smale condition Xiao, Yuming Zhu, Gaosheng Dynamical Systems In this paper, we prove the existence of periodic solutions with any prescribed minimal period $T>0$ for even second order Hamiltonian systems and convex first order Hamiltonian systems under the weak Nehari condition instead of Ambrosetti-Rabinowitz's. To this end, we shall develop the method of Nehari manifold to directly deal with a frequently occurring problem where the Nehari manifold is not a manifold. |
| title | The minimal periodic solutions for superquadratic autonomous Hamiltonian systems without the Palais-Smale condition |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2401.00655 |