  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.
