INVERSE SPECTRAL PROBLEM FOR STURM-LIOUVILLE OPERATOR WITH HIGHER ORDER POLYNOMIALS OF SPECTRAL PARAMETER IN THE BOUNDARY CONDITION

This paper is concerned with an inverse scattering problem for Sturm-Liouville operator with polynomials of spectral parameter in boundary condition. We provide scattering data and present some spectral properties. In order to study inverse scattering problem, the main equation is derived. As a consequence, we show that the potential can be recovered uniquely from scattering data.