Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Limit-point and limit-circle criteria for Sturm-Liouville equations with intermittently negative principal coefficients

W. N. Everitta1, I. W. Knowlesa2 and T. T. Reada3

a1 Department of Mathematics, University of Birmingham, Birmingham B15 2TT, England

a2 Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294, U.S.A.

a3 Department of Mathematics, Western Washington University, Bellingham, Washington 98225, U.S.A.

Synopsis

Limit-point and limit-circle criteria are given for the generalised Sturm-Liouville differential expression

S0308210500018874_eqnU1

where

(i) p, q, and w are real-valued on [a, b),

(ii) p−1, q, w are locally Lebesgue integrable on [a, b),

(iii) w > 0 almost everywhere on [a, b) and the principal coefficient p is allowed toassume both positive and negative values.

(Received January 15 1985)

(Revised January 09 1986)