Homoclinic orbits and periodic solutions for a class of Hamiltonian systems on time scales

In this paper, we are concerned with a second order non-autonomous Hamiltonian system on time scales T u Δ Δ ( ρ ( t ) ) + V u ( t , u ( t ) ) = f ( t ) , t ∈ T κ . Under certain conditions, the existence and multiplicity of periodic solutions are obtained for this Hamiltonian system on time scales by using the saddle point theory, the least action principle as well as the three-critical-point theorem. In addition, the existence of homoclinic orbit is obtained as a limit of 2 k T -periodic solutions of a given sequence of Hamiltonian system on time scales by means of the mountain pass theorem and the standard minimizing argument.