Periodic solutions of second order superquadratic Hamiltonian systems with potential changing sign (I)

We consider the periodic solutions of the second order Hamiltonian system-x¨-λx=h(t)V′(x)with V being positive and superquadratic at infinity, h being continuous, 2π-periodic, sign changing and satisfying {t|h(t)>0}¯∩{t|h(t)<0}¯=∅. Some existence and multiplicity results of periodic solutions are given.