Multiple periodic solutions of the second order Hamiltonian systems with superlinear terms

We study the existence of 2π-periodic solutions of the second order Hamiltonian systems − x ¨ − A ( t ) x = λ x + V x ′ ( t , x ) with superlinear terms and with saddle structure near the origin. Some multiplicity results are obtained by using bifurcation method, homological linking and Morse theory.