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Title: Further higher monotonicity properties of Sturm-Liouville functions (English)
Author: Došlá, Zuzana
Author: Háčik, Miloš
Author: Muldoon, Martin E.
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 29
Issue: 1
Year: 1993
Pages: 83-96
Summary lang: English
Category: math
Summary: Suppose that the function $q(t)$ in the differential equation (1) $y^{\prime \prime }+q(t)y=0 $ is decreasing on $(b,\infty )$ where $b \ge 0$. We give conditions on $q$ which ensure that (1) has a pair of solutions $y_1(t),\;y_2(t)$ such that the $n$-th derivative ($n\ge 1$) of the function $p(t)= y_1^2(t) +y_2^2(t)$ has the sign $(- 1)^{n+1}$ for sufficiently large $t$ and that the higher differences of a sequence related to the zeros of solutions of (1) are ultimately regular in sign. (English)
Keyword: n-times monotonic functions
Keyword: completely monotonic functions
Keyword: ultimately monotonic functions and sequences
Keyword: regularly varying functions
Keyword: Appell differential equation
Keyword: generalized Airy equation
Keyword: higher differences
MSC: 34B30
MSC: 34C10
MSC: 34D05
idZBL: Zbl 0812.34010
idMR: MR1242631
Date available: 2008-06-06T21:24:00Z
Last updated: 2012-05-10
Stable URL:
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