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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Main Author: Zhou Yuting
Format: Article
Language:English
Published: De Gruyter 2025-03-01
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.
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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