Scattering analysis of a quantum impulsive boundary value problem with spectral parameter

Abstract

We are interested in scattering and spectral analysis of an impulsive boundary value problem (IBVP) generated with a $q$-difference equation with eigenparameter in boundary condition in addition to impulsive conditions. We work on the Jost solution and scattering function of this problem, and by using the scattering solutions, we establish the resolvent operator, continuous spectrum and point spectrum of this problem. Furthermore, we discuss asymptotic behavior of the Jost solution and properties of eigenvalues.Also, we illustrate our results by a detailed example which is the special case of main problem.