Subharmonic solutions of first-order Hamiltonian systems
The aim of this article is to study subharmonic solutions of superquadratic and asymptotically (constant) linear nonautonomous Hamiltonian systems in R2n{{\mathbb{R}}}^{2n} respectively, and to improve the results in Professor Liu’s [Subharmonic solutions of Hamiltonian systems, Nonlinear Anal. 42 (...
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De Gruyter
2025-03-01
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| Series: | Advances in Nonlinear Analysis |
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| Online Access: | https://doi.org/10.1515/anona-2025-0074 |
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| author | Zhou Yuting |
| author_facet | Zhou Yuting |
| author_sort | Zhou Yuting |
| collection | DOAJ |
| description | The aim of this article is to study subharmonic solutions of superquadratic and asymptotically (constant) linear nonautonomous Hamiltonian systems in R2n{{\mathbb{R}}}^{2n} respectively, and to improve the results in Professor Liu’s [Subharmonic solutions of Hamiltonian systems, Nonlinear Anal. 42 (2000), no. 2, 185–198, Ser. A: Theory Methods]. For the TT-periodic Hamiltonian system, we show that for each integer j≥1j\ge 1, there exists a nonconstant jTjT-periodic solution xj{x}_{j} such that xj{x}_{j} and xpj{x}_{pj} (p∈Np\in {\mathbb{N}}) are geometrically distinct provided p>2np\gt 2n; for n=1n=1, xj{x}_{j} and xpj{x}_{pj} (p∈Np\in {\mathbb{N}}) are geometrically distinct provided p>1p\gt 1; if xj{x}_{j} is nondegenerate, then xj{x}_{j} and xpj{x}_{pj} (p∈Np\in {\mathbb{N}}) are geometrically distinct provided p>1p\gt 1. |
| format | Article |
| id | doaj-art-6e3cff4386d443798fad94564a80ceee |
| institution | OA Journals |
| issn | 2191-950X |
| language | English |
| publishDate | 2025-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj-art-6e3cff4386d443798fad94564a80ceee2025-08-20T01:54:16ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2025-03-0114153960310.1515/anona-2025-0074Subharmonic solutions of first-order Hamiltonian systemsZhou Yuting0School of Science, Tianjin University of Technology, Tianjin 300384, ChinaThe aim of this article is to study subharmonic solutions of superquadratic and asymptotically (constant) linear nonautonomous Hamiltonian systems in R2n{{\mathbb{R}}}^{2n} respectively, and to improve the results in Professor Liu’s [Subharmonic solutions of Hamiltonian systems, Nonlinear Anal. 42 (2000), no. 2, 185–198, Ser. A: Theory Methods]. For the TT-periodic Hamiltonian system, we show that for each integer j≥1j\ge 1, there exists a nonconstant jTjT-periodic solution xj{x}_{j} such that xj{x}_{j} and xpj{x}_{pj} (p∈Np\in {\mathbb{N}}) are geometrically distinct provided p>2np\gt 2n; for n=1n=1, xj{x}_{j} and xpj{x}_{pj} (p∈Np\in {\mathbb{N}}) are geometrically distinct provided p>1p\gt 1; if xj{x}_{j} is nondegenerate, then xj{x}_{j} and xpj{x}_{pj} (p∈Np\in {\mathbb{N}}) are geometrically distinct provided p>1p\gt 1.https://doi.org/10.1515/anona-2025-0074subharmonic solutionsmaslov-type indexsuperquadratic hamiltonian systemasymptotically linear hamiltonian system70h0534c2558e05 |
| spellingShingle | Zhou Yuting Subharmonic solutions of first-order Hamiltonian systems Advances in Nonlinear Analysis subharmonic solutions maslov-type index superquadratic hamiltonian system asymptotically linear hamiltonian system 70h05 34c25 58e05 |
| title | Subharmonic solutions of first-order Hamiltonian systems |
| title_full | Subharmonic solutions of first-order Hamiltonian systems |
| title_fullStr | Subharmonic solutions of first-order Hamiltonian systems |
| title_full_unstemmed | Subharmonic solutions of first-order Hamiltonian systems |
| title_short | Subharmonic solutions of first-order Hamiltonian systems |
| title_sort | subharmonic solutions of first order hamiltonian systems |
| topic | subharmonic solutions maslov-type index superquadratic hamiltonian system asymptotically linear hamiltonian system 70h05 34c25 58e05 |
| url | https://doi.org/10.1515/anona-2025-0074 |
| work_keys_str_mv | AT zhouyuting subharmonicsolutionsoffirstorderhamiltoniansystems |