Periodic solutions of superlinear autonomous Hamiltonian systems with prescribed period

In this paper we prove an existence theorem of nonconstant periodic solution of superlinear autonomous Hamiltonian system x˙(t)=J∇H(x(t)) with prescribed period under an assumption weaker than Ambrosetti-Rabinowitz-type condition:0<μH(x)⩽〈∇H(x),x〉,μ>2,|x|⩾R>0. Our result extends the pioneering work of Rabinowitz of 1978.