Morse homology of super-quadratic Hamiltonian systems on R2nR2n

We study periodic solutions of the Hamiltonian systemx′(t)=J∇H(t,x),x′(t)=J∇H(t,x), where J is the standard symplectic matrix, H is 2π-periodic in t and super-quadratic in x in some sense. Using the Morse homology theory developed in [A. Abbondandolo, P. Majer, Morse homology on Hilbert spaces, Comm. Pure Appl. Math. 54 (2001) 689–758], we get some existence results of periodic solutions.