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Strongly Singular Sturm – Liouville Problems
Author(s) -
Duhoux Michel
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200105)225:1<19::aid-mana19>3.0.co;2-9
Subject(s) - mathematics , sturm–liouville theory , eigenvalues and eigenvectors , operator (biology) , function (biology) , integrable system , pure mathematics , combinatorics , mathematical analysis , physics , boundary value problem , biochemistry , chemistry , repressor , quantum mechanics , evolutionary biology , biology , transcription factor , gene
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 ) = $\int_a^t$ (1/ r ) ds andchoose any c ∈] a , b [. We are interested in the eigenvalue problem Lu = λ m ( 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 ).