An examination of boundary value transmission problem with quadratic spectral parameter

Abstract

The main purpose of this study is to examine the properties of scattering solutions and scattering function of a difference equation subject to eigenparameter-dependent boundary and transmission conditions. In general, we are interested in a boundary value problem (BVP) generated by this difference equation, eigenparameter-dependent boundary and transmission conditions. Introducing the Jost solution and scattering solutions of BVP, we obtain the scattering function of this problem. Also, we find the resolvent operator, eigenvalues and continuous spectrum of the operator generated by this BVP. At the end, we present an example to demonstrate the effectiveness of our main results.