Computations of cohomology groups and nontrivial periodic solutions of Hamiltonian systems
type: Item
instance of: scholarly article
title: Computations of cohomology groups and nontrivial periodic solutions of Hamiltonian systems
zbMATH Open document ID: 1115.37056
author: Zhiqing Han
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-04-10T00:00:00Z
review text: In this paper \(2\pi\)-periodic solutions for the Hamiltonian system \(\dot z= JH(z,t)\) are investigated, where \(H(z,t)\in C^1(\mathbb{R}^{2N},\mathbb{R})\) is \(2\pi\)-periodic for \(t\) and \(J\) is the standard symplectic matrix. As in the classical infinite-dimensional Morse theory, the efficient application of the \({\mathcal E}\)-Morse theory depends on the computation of the critical groups at given critical points or infinity. By computing the \({\mathcal E}\)-critical groups at \(\theta\) and infinity of the corresponding functional of Hamiltonian systems, the existence of nontrivial periodic solutions for the systems which may be resonant at \(\theta\) and infinity under some new conditions is proved. Some results in the literature are extended and some new type of theorems are proved. The main tool is the \({\mathcal E}\)-Morse theory developed by \textit{W. Kryszewski} and \textit{A. Szulkin} [Trans. Am. Math. Soc.349, No. 8, 3181--3234 (1997; Zbl 0892.58015)] and Zou.
reviewed by: Vasile Marinca
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 5141580
zbMATH Keywords: \({\mathcal E}\)-Morse theory
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: periodic solutions
zbMATH Keywords: cohomology
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.07.047
OpenAlex ID: W2156824283
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DOI: 10.1016/J.JMAA.2006.07.047
description: scientific article; zbMATH DE number 5141580