Periodic solutions of superquadratic Hamiltonian systems with bounded forcing terms (Q1117083)

We prove the existence of infinitely many distinct T-periodic solutions of the forced Hamiltonian system \(\dot z={\mathcal I}(H_ z(z)+F_ z(t,z))\) under the conditions that H is \(C^ 1\) and superquadratic at infinity and that F is \(C^ 1\), T-periodic in time, bounded in \(C^ 0\), and having a gradient of at most polynomial growth at infinity. The proof of this qualitative results is based on minimax methods.