Periodic solutions of a non-coercive Hamiltonian system (Q1915561)

We study the existence of periodic solutions of the Hamiltonian system \(\dot x=J H'(t,x)\), where \(H\) is a non-coercive Hamiltonian of the type \(H(t,r,p)= f(|p-Ar|)+ h(t)\cdot (r,p)\), \(A\) is a matrix of order \(n\), \(h\) is a continuous function, and \(f:\mathbb{R}_+\to \mathbb{R}\) is a subquadratic differentiable function. Under some hypotheses over \(a\), \(h\), \(f\), and by using the dual least action principle, we prove that the above system has a nontrivial periodic solution.