A new approximation Sturm-Liouville problem

Abstract

In this paper, we study that inverse Sturm-Liouville problem having singularity of type q(x) = ? x + qp 0 (x) at zero point. We prove that the difference between two potential functions q(x) and ?q (x) becomes sufficiently small whenever the spectral datas {?n, ?n}?n=0 and {??n, ??n}?n=0 for q(x) and ?q (x) respectively are chosen sufficiently close to each other. © 2012 by the Mathematical Association of Thailand. All rights reserved.