Periodic solutions of superlinear autonomous Hamiltonian systems with prescribed period (Q855403)

We prove an existence theorem for nonconstant periodic solutions of the superlinear autonomous Hamiltonian system \(\dot x(t)=J\nabla H(x(t))\) with prescribed period under an assumption weaker than the Ambrosetti-Rabinowitz-type condition \[ 0<\mu H(x)\leq (\nabla H(x),x\rangle,\quad \mu>2,\;|x|\geq R>0. \] Our result extends the pioneering work of \textit{P. H. Rabinowitz} [Commun. Pure Appl. Math. 31, 156--184 (1978; Zbl 0358.70014)]