On impulsive Sturm–Liouville operators with Coulomb potential and spectral parameter linearly contained in boundary conditions

Abstract

The Sturm-Liouville problem with linear discontinuities is investigated in the case where an eigenparameter appears not only in a differential equation but also in boundary conditions. Properties and the asymptotic behavior of spectral characteristics are studied for the Sturm-Liouville operators with Coulomb potential that have discontinuity conditions inside a finite interval. Moreover, the Weyl function for this problem is defined and uniqueness theorems are proved for a solution of the inverse problem with respect to this function.C sin kx C˛ sin k.2d x/ for x > d;