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Erschienen in: Journal of Dynamical and Control Systems 2/2019

02.05.2018

Infinitely Many Rotating Periodic Solutions for Second-Order Hamiltonian Systems

verfasst von: Guanggang Liu, Yong Li, Xue Yang

Erschienen in: Journal of Dynamical and Control Systems | Ausgabe 2/2019

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Abstract

In this paper, we consider a class of second-order Hamiltonian system in \(\mathbb {R}^{N}\) with combined nonlinearities. We will study the multiplicity of rotating periodic solutions, i.e., \(x(t+T)=Qx(t)\) with \(T>0\) and Q is an \(N\times N\) orthogonal matrix. In the case \(Q^{k}\neq I_{N}\) for any positive integer k, such a rotating periodic solution is just a quasi-periodic solution; In the case \(Q^{k}=I_{N}\) for some positive integer k, such a rotating periodic solution is just a subharmonic solution. We will use the Fountain Theorem and its dual form to obtain two sequences of rotating periodic solutions with the corresponding energy tending to infinity and zero respectively.

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Metadaten
Titel
Infinitely Many Rotating Periodic Solutions for Second-Order Hamiltonian Systems
verfasst von
Guanggang Liu
Yong Li
Xue Yang
Publikationsdatum
02.05.2018
Verlag
Springer US
Erschienen in
Journal of Dynamical and Control Systems / Ausgabe 2/2019
Print ISSN: 1079-2724
Elektronische ISSN: 1573-8698
DOI
https://doi.org/10.1007/s10883-018-9402-2

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