A uniqueness theorem for Sturm-Liouville equations with a spectral parameter nonlinearly contained in the boundary condition

Abstract

In this work, we consider the inverse scattering problem for Sturm-Liouville equation on the semi-infinite interval with a nonlinear spectral parameter in the boundary condition. The scattering data of the problem is defined and the properties of the scattering data are investigated. The fundamental equation is obtained and uniqueness of the algorithm to the potential with given scattering data is studied.