Morse homology of super-quadratic Hamiltonian systems on R-2n

摘要

We study periodic solutions of the Hamiltonian system x'(t) = J del H (t, x), where J is the standard symplectic matrix, H is 2 pi-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. (c) 2008 Elsevier lnc. All rights reserved.