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Maximum and anti-maximum principles for singular Sturm–Liouville problems*

Published online by Cambridge University Press:  14 November 2011

M. Duhoux
M. Duhoux
Affiliation:
Institut de Mathématiques Pures et Appliquées, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium
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Abstract

The maximum and anti-maximum principles are extended to the case of eigenvalue Sturm–Liouville problems

with boundary conditions of Dirichlet type (if possible) on a bounded interval [a, b]. The function r is assumed to be continuous and > 0 on ]a, b[, but the function 1/r is not necessarily integrable on [a, b]. The conditions on the functions p, m and h depend on the integrability or nonintegrability of 1/r on [a, c] and/or [c, b], for some c ∈ ]a, b[. The weight function m is not necessarily of constant sign.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 3 , 1998 , pp. 525 - 547
Copyright
Copyright © Royal Society of Edinburgh 1998

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