Periodic solutions for a class of non-autonomous Hamiltonian systems Original Research Article

We consider the existence of nontrivial periodic solutions for a superlinear Hamiltonian system: View the MathML source(H)Ju˙-A(t)u+∇H(t,u)=0,u∈R2N,t∈R. Turn MathJax on 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: View the MathML source0<μH(t,u)⩽u·∇H(t,u),μ>2,|u|⩾R>0. Turn MathJax on 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).