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Abstract: In this paper, we study the Sobolev’s spaces on time scales and their properties. As applications, we present a recent approach via variational methods and the critical point theory to obtain the existence of solutions for a class of second order Hamiltonian systems on time scales. By establishing a proper variational setting, three existence results for systems under consideration are obtained. Finally, three examples are presented to illustrate the feasibility and effectiveness of the existence results. [Copyright &y& Elsevier]

Abstract: In this paper, a class of second-order Hamiltonian systems with impulsive effects are considered. We establish some sufficient conditions for the existence of solutions for the second-order Hamiltonian systems with impulsive effects where , , are continuous and . The solutions are sought by means of some critical point theorems. Finally, two examples are presented to illustrate the feasibility and effectiveness of our results. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the existence and multiplicity of solutions for some Dirichlet impulsive problems and some existence and multiplicity results are obtained. The solutions are sought by means of Lax–Milgram theorem and some critical theorems. [Copyright &y& Elsevier]