✦ LIBER ✦
Prüfer angle asymptotics for Atkinson's semi-definite Sturm–Liouville eigenvalue problem
✍ Scribed by Paul Binding; Hans Volkmer
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 217 KB
- Volume
- 278
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
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)