A hochstadt-lieberman theorem for integro-differential operator

In this study, we solve a half inverse problem for integro-differential operator that consists of Sturm-Liouville differential part and integral part of Volterra type on a finite interval by using Hochstadt-Lieberman's method. We consider that q is a squared integrable function on [0, φ] and the kernel of the integral perturbation is integrable on its domain. Especially, we show that the potential function q is known as uniquely when the kernel of the integral perturbation is given. © 2013 Academic Publications, Ltd.