Existence of Periodic Solutions of Linear Hamiltonian Systems with Sublinear Perturbation

Zhiqing Han

doi:10.1155/2010/945421

Research Article

Open Access

Existence of Periodic Solutions of Linear Hamiltonian Systems with Sublinear Perturbation

Zhiqing Han¹Email author

Boundary Value Problems20102010:945421

https://doi.org/10.1155/2010/945421

Received: 2 June 2009

Accepted: 19 March 2010

Published: 6 April 2010

Abstract

We investigate the existence of periodic solutions of linear Hamiltonian systems with a nonlinear perturbation. Under generalized Ahmad-Lazer-Paul type coercive conditions for the nonlinearity on the kernel of the linear part, existence of periodic solutions is obtained by saddle point theorems. A note on a result of Rabinowitz is also given.

Keywords

Differential EquationPartial Differential EquationOrdinary Differential EquationPeriodic SolutionFunctional Equation

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Authors’ Affiliations

(1)

School of Mathematical Sciences, Dalian University of Technology, Dalian, China

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This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.