UNIQUENESS OF THE SOLUTION OF HALF INVERSE PROBLEM FOR THE IMPULSIVE STURM LIOUVILLE OPERATOR

Abstract

The half-inverse spectral problem for an impulsive Sturm-Liouville operator consists in reconstruction of this operator from its spectrum and half of the potential. In this study, the spectrum of the impulsive Sturm-Liouville problem is given and by using the Hochstadt and Lieberman's method we show that if q(x) is prescribed on (0, pi/2), then only one spectrum is sufficient to determine q(x) on the interval (0, pi) for this problem