Periodic solutions for a class of non-autonomous Hamiltonian systems

We consider the existence of nontrivial periodic solutions for a superlinear Hamiltonian system:(H)Ju˙-A(t)u+∇H(t,u)=0,u∈R2N,t∈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<μH(t,u)⩽u·∇H(t,u),μ>2,|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).