Periodic solutions for some nonautonomous second order Hamiltonian systems
type: Item
instance of: scholarly article
title: Periodic solutions for some nonautonomous second order Hamiltonian systems
zbMATH Open document ID: 1142.37023
author: Yiwei Ye
author: Chun-Lei Tang
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-05-28T00:00:00Z
review text: In this paper, the second order Hamiltonian systems: \[ \ddot u(t)= \nabla F(t,u(t))\;\text{a.e. }t\in[0,T], \qquad u(0)-u(T)= \dot u(0)-\dot u(T)=0, \] where \(T>0\) and \(F:[0,T]\times\mathbb R^N\to\mathbb R\) is measurable in \(t\) for every \(x\in\mathbb R^N\) and continuously differentiable in \(u\) for a.e. \(t\in [0,T]\), and there exist \(a\in C(\mathbb R^+,\mathbb R^+)\), \(b\in L^1(0,T;\mathbb R^+)\) such that \(|F(t,x)|\leq a(|x|)b(t)\), \(|\nabla F(t,x)|\leq a(|x|)b(t)\) for all \(x\in\mathbb R^N\) and a.e. \(t\in[0,T]\) is considered. The existence and multiplicity of periodic solutions are obtained for these systems by minimax methods in critical point theory.
reviewed by: Vasile Marinca
Mathematics Subject Classification ID: 37C60
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 5279806
zbMATH Keywords: periodic solution
zbMATH Keywords: second-order Hamiltonian system
zbMATH Keywords: saddle point theorem
zbMATH Keywords: generalized mountain pass theorem
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.03.021
OpenAlex ID: W2080638159
cites work: Q3739492
cites work: On the solvability of semilinear gradient operator equations
cites work: On the periodic nonlinearity and the multiplicity of solutions
cites work: On periodic solutions of superquadratic Hamiltonian systems
cites work: Periodic solutions to differential systems with unbounded or periodic nonlinearities
cites work: Periodic and subharmonic solutions of a class of subquadratic second-order Hamiltonian systems
cites work: Applications of local linking to critical point theory
cites work: A generalized saddle point theorem
cites work: Periodic solutions of nonautonomous second order Hamiltonian systems
cites work: Q3791764
cites work: Critical point theory and Hamiltonian systems
cites work: Periodic solutions for some nonautonomous second-order systems
cites work: Q3749777
cites work: Periodic non-autonomous second-order dynamical systems
cites work: Periodic solutions of non-autonomous second order systems with \(\gamma\)- quasisubadditive potential
cites work: Periodic solutions for nonautonomous second order systems with sublinear nonlinearity
cites work: A note on periodic solutions of nonautonomous second-order systems
cites work: Periodic solutions for second order systems with not uniformly coercive potential
cites work: Notes on periodic solutions of subquadratic second order systems.
cites work: Periodic solutions for second order Hamiltonian systems with a change sign potential
cites work: Periodic and subharmonic solutions of second-order Hamiltonian systems
cites work: Periodic solutions for a class of superquadratic Hamiltonian systems
cites work: Q3940913
cites work: Periodic solutions for nonautonomous second-order systems with bounded nonlinearity
DOI: 10.1016/J.JMAA.2008.03.021
description: scientific article; zbMATH DE number 5279806