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Open Access 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

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.