Nontrivial periodic solutions for strong resonance Hamiltonian systems
type: Item
instance of: scholarly article
title: Nontrivial periodic solutions for strong resonance Hamiltonian systems
zbMATH Open document ID: 0881.34061
DOI: 10.1016/S0294-1449(97)80150-3
author: O. Diekmann
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1998-02-25T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78402
review text: A nonautonomous Hamiltonian system of the form \[ -J{dx\over dt}= H_x(t,x), \] where \(H\in C^2([0,1]\times \mathbb{R}^{2n},\mathbb{R})\) is 1-periodic in \(t\) and \[ J=\begin{pmatrix} 0 & -I_n\\ I_n & 0\end{pmatrix} \] is considered. Under the assumption that the Hamiltonian has an asymptotically linear gradient and the linearized operators have distinct Maslov indices at \(0\) and at infinity it is proved the existence of nontrivial periodic solutions.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 70K30
zbMATH DE Number: 1019547
zbMATH Keywords: strong resonance
zbMATH Keywords: nonautonomous Hamiltonian system
zbMATH Keywords: Maslov indices
zbMATH Keywords: nontrivial periodic solutions
reviewed by: Sergei Georgievich Zhuravlev
MaRDI profile type: Publication
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Wikidata QID: Q127725485
OpenAlex ID: W2079209998
description: scientific article; zbMATH DE number 1019547