Inverse problems for impulsive Sturm-Liouville operator with spectral parameter linearly contained in boundary conditions

Abstract

In this work, the Sturm-Liouville problem, with discontinuities in the case when an eigenparameter appears not only in the differential equation but also in one of the boundary conditions, is studied. The spectrum and the resolvent operator of this problem are given. Moreover, the Weyl function for this problem under consideration has been defined and uniqueness theorems for the solution of the inverse problem according to this function and spectral data have been proved.