Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

A note on a paper of Atkinson concerning the asymptotics of an eigenvalue problem with interior singularity

B.J. Harrisa1

a1 Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115–2888, U.S.A.

Synopsis

In [2] Atkinson considers the asymptotic form of the eigenvalues of the linear differentialequation

S0308210500024859_eqn1

where a < 0 < b and y satisfies appropriate conditions at a andb. In particular Atkinson considers where q is singular at 0. In this case q(x) = xK, his results cover the case l ≦ K < . We extend Atkinson's results to cover more singular q, in the power case 1 ≦K <

(Received October 05 1987)

(Revised February 16 1988)