An interior inverse problem for the Sturm–Liouville operator with discontinuous conditions

In this work, we study the inverse problem for the Sturm–Liouville operator − D 2 + q with discontinuity boundary conditions inside a finite closed interval. Using spectral data of a kind, it is shown that the potential function q ( x ) can be uniquely determined by a set of values of eigenfunctions at some internal point and one spectrum.