Multiple periodic solutions of hamiltonian systems confined in a box

We consider a nonautonomous Hamiltonian system, T-periodic in time, possibly defined on a bounded space region, the boundary of which consists of singularity points which can never be attained. Assuming that the system has an interior equilibrium point, we prove the existence of infinitely many T-periodic solutions, by the use of a generalized version of the Poincaré–Birkhoff theorem.