Scattering theory of the quadratic eigenparameter depending impulsive Sturm–Liouville equations

Abstract

We handle an impulsive Sturm–Liouville boundary value problem. We find the Jost solution, Jost function, and scattering function of this problem and examine the properties of scattering function. We also study eigenvalues and resolvent operator of this problem. Finally, we exemplify our work by taking a different problem.