Sat, Murat; Yilmaz, Emrah

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.

Sat, M.; Panakho, Es.

Inverse nodal problems consist in constructing operators from the given nodes (zeros) of their eigenfunctions. In this study, we have estimated nodal points and nodal lengths for the Sturm-Liouville operators with Coulomb potential. Furthermore, by using nodal points (zeros of eigenfunctions), we have shown that the potential function of the Sturm-Liouville operators with Coulomb potential can be established uniquely. AMS Subject Classification: 34A55, 34L05, 45C05