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

Abstract

This paper deals with the singular Sturm-Liouville expressions egin{eqnarray} ell y equiv -y''+q(x)y=lambda y end{eqnarray} 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