A non-autonomous Hamiltonian system on time scales

In this paper we are concerned with a second order non-autonomous Hamiltonian system on time scales TT of the form {uΔ2(t)=∇F(σ(t),uσ(t)),Δ-a.e.t∈[0,T]Tκ,u(0)−u(T)=0,uΔ(0)−uΔ(T)=0. Some results on the existence and multiplicity of periodic solutions are obtained for the Hamiltonian system by means of the saddle point theorem, the least action principle as well as the three-critical-point theorem.