Bull. Korean Math. Soc. 2013; 50(2): 499-506
Printed March 31, 2013
https://doi.org/10.4134/BKMS.2013.50.2.499
Copyright © The Korean Mathematical Society.
A. Sinan Ozkan, Baki Keskin, and Yasar Cakmak
Cumhuriyet University, Cumhuriyet University, Cumhuriyet University
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
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