Existence and multiplicity of periodic solutions for a class of second-order Hamiltonian systems

Westudy the existence and multiplicity of periodic solutions of the following second-order Hamiltonian system Ru.t/ C rT􀀀K.t; u.t// C W.t; u.t//U D 0: The existence of a nontrivial periodic solution is obtained when rW is asymptotically linear at infinity, and the existence of infinitely many periodic solutions is also obtained when rW is superlinear.