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

Abstract

SynopsisIn [2] Atkinson considers the asymptotic form of the eigenvalues of the linear differentialequationwhere 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 <