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Open Access Open Badges Research Article

Existence of Periodic Solutions of Linear Hamiltonian Systems with Sublinear Perturbation

Zhiqing Han

Author Affiliations

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

Boundary Value Problems 2010, 2010:945421  doi:10.1155/2010/945421

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2010/1/945421

Received:2 June 2009
Revisions received:4 February 2010
Accepted:19 March 2010
Published:6 April 2010

© 2010 The Author(s).

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.

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