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Strongly Singular Sturm – Liouville Problems

✍ Scribed by Michel Duhoux

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
238 KB
Volume
225
Category
Article
ISSN
0025-584X

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✦ Synopsis

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) = t a (1/r) ds and choose any c ∈ ]a, b[ . We are interested in the eigenvalue problem Lu = λm(t)u, u(a) = u(b) = 0, and the corresponding maximal and anti -maximal principles, in the situation when 1/r ∈ L 1 (a, c), 1/r ∈ L 1 (c, b), pr 1 ∈ L 1 (a, c) and pr 1 ∈ L 1 (c, b).

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