Scattering properties of Sturm-Liouville equations with sign-alternating weight and transmission condition at turning point

Abstract In this article, we focus on the scattering analysis of Sturm-Liouville type singular operator including an impulsive condition and turning point. In the classical literature, there are plenty of papers considering the positive values of the weight function in both continuous and discontinuous cases. However, this article differs from the others in terms of the impulsive condition appearing at the turning point. We generate the scattering function, resolvent operator, and discrete spectrum of the operator using the hyperbolic representations of the fundamental solutions. Finally, we create an example to show the article’s primary conclusions.