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Prüfer angle asymptotics for Atkinson's semi‐definite Sturm–Liouville eigenvalue problem
Author(s) -
Binding Paul,
Volkmer Hans
Publication year - 2005
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/mana.200410315
Subject(s) - mathematics , sturm–liouville theory , eigenvalues and eigenvectors , mathematical analysis , oscillation (cell signaling) , integrable system , order (exchange) , boundary value problem , mathematical physics , pure mathematics , function (biology) , differential equation , chemistry , physics , quantum mechanics , biochemistry , finance , evolutionary biology , economics , biology
Atkinson's semi‐definite Sturm–Liouville problem consists of the differential equation –( y ′/ s )′ + qy = λry , with s , q , r integrable on [ a , b ], q real‐valued, s, r ≥ 0, and separated boundary conditions at a, b . The asymptotic behavior of the associated Prüfer angle is determined as λ → ±∞. This leads to existence theorems for eigenvalues λ n with prescribed oscillation number n and their asymptotics. In general, λ n grows faster than n 2 , and the order of the corresponding characteristic function is less than ½. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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