Bulletin of the
Korean Mathematical Society BKMS

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

Keywords: Sturm-Liouville operator, determination of the potential, discontinuous condition, half inverse problem

MSC numbers: 34A55, 34B24, 34L05, 45C05