Spectral singularities of an impulsive Sturm-Liouville operators

In this paper, we handle an impulsive Sturm–Liouville equation with complex potential on the semi axis. The objective of this work is to examine some spectral properties of this impulsive Sturm–Liouville equation. By the help of a transfer matrix B, we obtain Jost solution of this problem. Furthermore, using Jost solution, we find Green function and resolvent operator of this equation. Finally, we consider two unperturbated impulsive Sturm–Liouville operators. We examine the eigenvalues and spectral singularities of these problems.