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 Equation
Partial Differential Equation
Ordinary Differential Equation
Periodic Solution
Functional Equation

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Authors’ Affiliations

(1)

School of Mathematical Sciences, Dalian University of Technology, Dalian, 116023, Liaoning, China

Copyright

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.