Scattering Function and The Resolvent of The Impulsive Boundary Value Problem

The purpose of this study is to examine the properties of scattering solutions and the scattering function of an impulsive Sturm-Liouville boundary value problem on the semi axis. By using Jost solutions, we obtain the scattering function, asymptotic representation of Jost function and resolvent operator. Finally, we study scattering solutions and scattering function of an unperturbated impulsive equation.