Variational approaches to impulsive elastic beam equations of Kirchhoff type

In this paper, we study the existence of multiple solutions for impulsive fourth- order differential equations of Kirchhoff type. Using a variational method and some critical points theorems, we obtain some new criteria for guaranteeing that impulsive fourth-order differential equations of Kirchhoff type have three and infinitely many solutions. Some recent results are extended and improved. Some examples are presented to demonstrate the applications of our main results.