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

İngilizce (OpenAlex)

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, ${\frac{\pi}{2}}$ ), then only one spectrum is sufficient to determine $q(x)$ on the interval (0, ${\pi}$ ) for this problem.