Periodic and subharmonic solutions for a class of superquadratic Hamiltonian systems
type: Item
instance of: scholarly article
title: Periodic and subharmonic solutions for a class of superquadratic Hamiltonian systems
zbMATH Open document ID: 1063.34033
author: Zeng-Qi Ou
author: Chun-Lei Tang
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-09-23T00:00:00Z
review text: The authors prove two existence theorems for periodic solutions of a Hamiltonian system of the form \[ -J \dot{u}=\nabla H(t,u), \] where \(u \in \mathbb R^{2n}\), \(J\) is the symplectic matrix and \(H\) a Hamiltonian function \(T\)-periodic in \(t\). In the first theorem, under some conditions on \(H\), they show the existence of at least one nontrivial \(T\)-periodic solution. In the second theorem, they show the existence of infinitely many subharmonic solutions. In their proofs, they use the generalized mountain pass theorem and a theorem due to \textit{S. Li} and \textit{A. Shujie} [J. Differ. Equations 112, No.1, 226-238 (1994; Zbl 0807.58040)].
reviewed by: Faouzi Lakrad
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37J45
zbMATH DE Number: 2102582
zbMATH Keywords: periodic and subharmonic solutions
zbMATH Keywords: superquadratic
zbMATH Keywords: Hamiltonian
MaRDI profile type: Publication
full work available at URL: j.na.2004.03.029
OpenAlex ID: W2030344039
cites work: Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
cites work: Q4292197
cites work: Subharmonic solutions of Hamiltonian systems
cites work: A unified approach to a class of strongly indefinite functionals
cites work: Periodic Solutions of Hamiltonian Systems
cites work: On periodic solutions of superquadratic Hamiltonian systems
cites work: Periodic solutions of ''superquadratic'' Hamiltonian systems
cites work: Periodic solutions for a class of nonautonomous Hamiltonian systems
cites work: Applications of local linking to critical point theory
cites work: Critical point theory and Hamiltonian systems
cites work: Periodic solutions of hamiltonian systems
cites work: On subharmonic solutions of hamiltonian systems
cites work: Q3749777
DOI: 10.1016/J.NA.2004.03.029
description: scientific article; zbMATH DE number 2102582