Existence of Periodic Solutions of Linear Hamiltonian Systems with Sublinear Perturbation
School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, Liaoning, China
Boundary Value Problems 2010, 2010:945421 doi:10.1155/2010/945421Published: 6 April 2010
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.