Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian system

Abstract

In this article, we study the existence of non-zero periodic solutions for Hamiltonian systems with impulsive conditions. By using a variational method and a variant fountain theorem, we obtain new criteria to guarantee that the system has at least one non-zero periodic solution or infinitely many non-zero periodic solutions. However, without impulses, there is no non-zero periodic solution for the system under our conditions.

Keywords

• Impulsive differential equations
• critical point theory
• periodic solution
• variant fountain theorems