Variational methods to the second-order impulsive differential equation with Dirichlet boundary value problem

In this paper, we study the existence of solutions for a class of second-order impulsive differential equation. By using the critical point theorem of Y. Jabri and an even functional theorem, we give some new criteria to guarantee that the impulsive differential equation has at least one solution, infinitely many solutions under the assumption that a nonlinear term satisfies sublinear, superlinear, asymptotically linear, respectively. Some recent results are extended and conditions of assumptions are simplified. Finally, some examples are presented to illustrate our main results.