Boundary Value Problems
Volume 2010 (2010), Article ID 945421, 12 pages
Research Article

Existence of Periodic Solutions of Linear Hamiltonian Systems with Sublinear Perturbation

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

Received 2 June 2009; Revised 4 February 2010; Accepted 19 March 2010

Academic Editor: Ivan T. Kiguradze

Copyright © 2010 Zhiqing Han. 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.


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.