Continuity of the scattering function and Levinson type formula for Klein-Gordon s-wave equation with boundary conditon depends on spectral parameter

Abstract

In this article, we consider inverse problem of scattering theory for Klein-Gordon s-wave equation with boundary condition depends on spectral parameter. We define the scattering data and we also prove that the continuity of the scattering function discussing the scattering solutions. Furthermore, we obtain Levinson type formula.