Periodic solutions of some resonant Hamiltonian systems

Based on the Galerkin approximation and the Morse inequality, an existence theorem of periodic solutions of the Hamiltonian systemJz′=H′(t,z)Jz′=H′(t,z) is given, where H′(t,z)H′(t,z) is asymptotically linear and resonant at infinity. Existence of periodic solutions of the resonant asymmetric p-Laplacian equation is also discussed.