IJPAM: Volume 88, No. 3 (2013)

A HOCHSTADT-LIEBERMAN THEOREM FOR
INTEGRO-DIFFERENTIAL OPERATOR

Murat Sat$^1$, Emrah Yilmaz$^2$
$^1$Department of Mathematics
Erzincan University
Erzincan, 24100, TURKEY
$^2$Department of Mathematics
Firat University
Elazıg, 23119, TURKEY


Abstract. 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 $[0,\pi]$ 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.

Received: July 16, 2013

AMS Subject Classification: 34B24, 34K29

Key Words and Phrases: integro-differential equation, half inverse problem

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DOI: 10.12732/ijpam.v88i3.9 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 88
Issue: 3