On the spectral and scattering properties of eigenparameter dependent discrete impulsive Sturm–Liouville equations

Abstract

This work develops scattering and spectral analysis of a discrete impulsive Sturm–Liouville equation withspectral parameter in boundary condition. Giving the Jost solution and scattering solutions of this problem, we findscattering function of the problem. Discussing the properties of scattering function, scattering solutions, and asymptoticbehavior of the Jost solution, we find the Green function, resolvent operator, continuous and point spectrum of theproblem. Finally, we give an example in which the main results are made explicit.