The stability of the solution of an inverse spectral problem with a singularity

Abstract

‎This paper deals with the singular Sturm-Liouville expressions‎ <br />‎$ <br />‎ell y =‎ -‎y''+q(x)y=lambda y‎ <br />‎$‎ <br />‎on a finite interval‎, ‎where the potential function $q$ is real and‎ <br />‎has a singularity inside the interval‎. <br />‎Using the asymptotic estimates of a‎ <br />‎spectral fundamental system of solutions of Sturm-Liouville‎ <br />‎equation‎, ‎the asymptotic form of the solution of the‎ <br />‎equation (0.1) and the eigenvalues are obtained‎, ‎and proves the stability of the‎ <br />‎solution of the inverse spectral problem.