Periodic solutions for a class of non-autonomous Hamiltonian systems

We consider the existence of nontrivial periodic solutions for a superlinear Hamiltonian system: (H) j u - A (t)u + &DEL; H(t, u)=0, u ε R-,(2N) t ε R. We prove an abstract result on the existence of a critical point for a real-valued functional on a Hilbert space via a new deformation theorem. Different from the works in the literature, the new deformation theorem is constructed under the Cerami-type condition instead of Palais-Smale-type condition. In addition, the main assumption here is weaker than the usual Ambrosetti-Rabinowitz-type condition: 0 < μ H(t, u) ≤ u • &DEL; H (t, u). | u| ≥ R > 0. This result extends theorems given by Li and Willem (J. Math. Anal. Appl. 189 (1995) 6-32) and Li and Szulkin (J. Differential Equations 112 (1994) 226-238). © 2005 Elsevier Ltd. All rights reserved.