New existence and multiplicity theorems of periodic solutions for non-autonomous second order Hamiltonian systems

In the present paper, the non-autonomous second order Hamiltonian systems equation(1){ü(t)=∇F(t,u(t)),a.e. t∈[0,T]u(0)−u(T)=u̇(0)−u̇(T)=0, are studied and a new existence theorem and a new multiplicity theorem of periodic solutions are obtained.