Existence of periodic solutions of linear Hamiltonian systems with sublinear perturbation
type: Item
instance of: scholarly article
title: Existence of periodic solutions of linear Hamiltonian systems with sublinear perturbation
zbMATH Open document ID: 1201.37093
DOI: 10.1155/2010/945421
published in: Boundary Value Problems
publication date: 2010-06-24T00:00:00Z
full work available at URL: https://eudml.org/doc/227603
review text: The author considers a Hamiltonian system \(\dot u = JA(t)u+J\nabla G(u,t)\), where \(J\) is the standard symplectic matrix, \(A\) is a symmetric \(2N\times 2N\)-matrix with \(2\pi\)-periodic entries, \(G\) is \(2\pi\)-periodic in \(t\) and \(\nabla G\) has sublinear growth as \(|u|\to\infty\). The main result asserts that if \(G\) satisfies a kind of Ahmad-Lazer-Paul condition on the kernel of the linear part, then this system has a \(2\pi\)-periodic solution. Two more related results are also given. The arguments are variational and use a saddle point theorem of Benci and Rabinowitz.
reviewed by: Andrzej Szulkin
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 58E30
zbMATH DE Number: 5725777
zbMATH Keywords: Ahmad-Lazer-Paul condition
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: periodic solution
zbMATH Keywords: saddle point
Wikidata QID: Q59249882
author: Zhiqing Han
MaRDI profile type: Publication
OpenAlex ID: W1964738225
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description: scientific article; zbMATH DE number 5725777