a1 Department of Mathematics, University of Toronto, Toronto, Canada
a2 Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, U.S.A.Synopsis
Asymptotic formulae for the positive eigenvalues of a limit-circle eigenvalue problem for –y” + qy = λy on the finite interval (0, b] are obtained for potentials q which are limit circle and non-oscillatory at x = 0, under the assumption xq(x)∈L1(0,6). Potentials of the form q(x) = C/xk, 0<fc<2, are included. In the case where k = 1, an independent check based on the limit-circle theory of Fulton and an asymptotic expansion of the confluent hypergeometric function, M(a, b; z), verifies the main result.
(Received February 14 1984)
* This research was sponsored by the National Science Foundation under grant #MCS-7902025.