Periodic solutions generated by impulses for second-order Hamiltonian system with convexity potential

Abstract

In this paper, a class of second-order Hamiltonian systems with impulsive effects are considered. By using critical point theory, we obtain some new existence theorems of periodic solutions generated by impulses. Here, a solution of the Second-order Hamiltonian System with the impulsive condition is said to be generated by impulses if the System does not possess any solution without the impulsive condition. To the best of the authors’ knowledge, there are still few results in the literature to consider periodic solutions generated by impulses. Based on the facts mentioned above, in this paper we study the existence of periodic solutions generated by impulses with convexity potential.