Perturbation of Domain: Ordinary Differential Equations

Abstract

We work with the Friedrichs extension of a one dimensional Schrodinger whose potential has a certain type of regular singularity near one end point. We study the effect on the eigenvalues of shrinking the region slightly near the end point. In particular we calculate the rate at which the eigenvalues of the smaller region converge to the eigenvalues of the larger region as the region expands. A result of this type was needed by that author in another paper concerned with a domain perturbation problem on Riemannian manifolds. The problem here, however, is stated purely in terms of ordinary differential equations.

9 Pages. Shortened version to improve clarity. To appear Proc. Roy. Soc. Edinburgh Sect. A. Proof of Theorem 3.1 expanded slightly