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

Published online by Cambridge University Press:  14 November 2011

W. N. Everitt ,
I. W. Knowles  and
T. T. Read
W. N. Everitt
Affiliation:
Department of Mathematics, University of Birmingham, Birmingham B15 2TT, England
I. W. Knowles
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294, U.S.A.
T. T. Read
Affiliation:
Department of Mathematics, Western Washington University, Bellingham, Washington 98225, U.S.A.
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Synopsis

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

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 3-4 , 1986 , pp. 215 - 228
Copyright
Copyright © Royal Society of Edinburgh 1986

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