Multiple Solutions for a Second-Order Impulsive Sturm-Liouville Equation

Abstract

We study the existence of solutions to a boundary value problem of a second-order impulsive Sturm-Liouville equation with a control parameter $\lambda$. By employing some existing critical point theorems, we find the range of the control parameter in which the boundary value problem admits at least three solutions. It is also shown that, under certain conditions, there exists an interval of the control parameter in which the boundary value problem possesses infinitely many solutions. Some examples are given to demonstrate the main results in this paper.