New existence of periodic solutions for second order non-autonomous Hamiltonian systems
type: Item
instance of: scholarly article
title: New existence of periodic solutions for second order non-autonomous Hamiltonian systems
zbMATH Open document ID: 1201.37094
author: Qiongfen Zhang
author: X. H. Tang
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-07-07T00:00:00Z
review text: The authors consider the second order Hamiltonian system \(\ddot x(t)-B(t)x(t)+\nabla H(t,x)=0\). They show that under some conditions on \(B\) and \(H\) this system has a nontrivial periodic solution. The results extend those contained in [\textit{X. M. He} and \textit{X. Wu}, J. Math. Anal. Appl. 341, No. 2, 1354--1364 (2008; Zbl 1133.37025)]. The proofs use a linking and a local linking argument for the Euler-Lagrange functional corresponding to the problem.
reviewed by: Andrzej Szulkin
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 5731692
zbMATH Keywords: periodic solution
zbMATH Keywords: linking theorem
zbMATH Keywords: local linking theorem
zbMATH Keywords: second order Hamiltonian system
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.03.033
OpenAlex ID: W2019405736
cites work: Q4292197
cites work: Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems
cites work: Multiple periodic solutions for second order systems with changing sign potential
cites work: Applications of local linking to critical point theory
cites work: On periodic solutions of superquadratic Hamiltonian systems
cites work: Periodic non-autonomous second-order dynamical systems
cites work: Periodic solutions of second-order nonautonomous dynamical systems
cites work: Critical point theory and Hamiltonian systems
cites work: Existence of homoclinic solution for the second order Hamiltonian systems.
cites work: Q3749777
cites work: Notes on periodic solutions of subquadratic second order systems.
cites work: Periodic and subharmonic solutions of second-order Hamiltonian systems
cites work: Saddle point characterization and multiplicity of periodic solutions of non-autonomous second-order systems
cites work: Periodic solutions for a class of nonautonomous second-order systems
cites work: Infinitely many solutions for Hamiltonian systems
cites work: Periodic solutions for a class of nonautonomous second order Hamiltonian systems
cites work: Existence of periodic solutions to second-order Hamiltonian systems with potential indefinite in sign
cites work: Homoclinic solutions for a class of second-order Hamiltonian systems
cites work: Homoclinic solutions for a class of the second order Hamiltonian systems
cites work: Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential
cites work: Dual variational methods in critical point theory and applications
cites work: Critical point theory for indefinite functionals with symmetries
cites work: Periodic solutions of second order non-autonomous Hamiltonian systems with local superquadratic potential
DOI: 10.1016/J.JMAA.2010.03.033
description: scientific article; zbMATH DE number 5731692