On the Investigation for Discontinuous Sturm-Liouville Operator of Scattering Theory

Abstract

This paper deals with the investigation on the direct scattering problem for
Sturm-Liouville operator containing both the discontinuous coefficient and the discontinuity conditions at some point on the positive half line. The integral representation of Jost solution is obtained and the properties of its kernel function are given. A total collection of the scattering data is constructed and the behavior of the scattering function at infinity is examined.