Summary: We consider the existence of nontrivial periodic solutions for the superlinear Hamiltonian system
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 work in the literature, the new deformation theorem is constructed under a Cerami-type condition instead of Palais-Smale-type condition. In addition, the main assumption here is weaker than the usual Ambrosetti-Rabinowitz-type condition
This result extends theorems given by S. J. Li and M. Willem [J. Math. Anal. Appl. 189, 6–32 (1995; Zbl 0820.58012)] and S. J. Li and A. Szulkin [J. Differ. Equations 112, 226–238 (1994; Zbl 0807.58040)].