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. © 2005 Elsevier Inc. All rights reserved.