Inverse problems for the impulsive Sturm-Liouville operator with jump conditions

Abstract

The inverse problem for impulsive Sturm-Liouville operators with discontinuity conditions is considered. We have shown that all parameters used in the boundary conditions as well as can be uniquely established by a set of values of eigenfunctions at the mid-point and one spectrum. Moreover, we discuss Gesztesy-Simon theorem and show that if the potential function is prescribed on the interval for some , then parts of a finite number of spectra suffice to determine on .