Strongly singular Sturm-Liouville problems

Duhoux, Michel
(2001) Mathematische Nachrichten — Vol. 225, p. 19-38 (2001)

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  • Duhoux, MichelUCLouvain
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Abstract
We consider a Sturm- Liouville operator Lu = - (r(t)u ')' + p(t)u, where r is a (strictly) positive continuous function on ]a, b[ and p is locally integrable on ]a, b[. Let r(1)(t) = integral (t)(a)(1/r) ds and choose any c is an element of ]a, b[. We are interested in the eigenvalue problem Lu = lambdam(t)u, u(a) = u(b) = 0, and the corresponding maximal and anti-maximal principles, in the situation when 1/r is an element of L-1(a, c), 1/r is not an element of L-1(c, b), pr(1) is not an element of L-1 (a, c) and pr(1) is not an element of L-1(c, b).
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Duhoux, M. (2001). Strongly singular Sturm-Liouville problems. Mathematische Nachrichten, 225, 19-38. https://doi.org/10.1002/1522-2616(200105)225:1<19::AID-MANA19>3.0.CO;2-9 (Original work published 2001)