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

Document Type : Research Paper

Author

Department of Pure Mathematics‎, ‎Faculty of‎ ‎Mathematical Sciences‎, ‎University of Kashan‎, ‎Kashan‎, ‎Iran

Abstract

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

Keywords

Main Subjects

### History

• Receive Date: 29 December 2013
• Revise Date: 07 July 2014
• Accept Date: 08 July 2014