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Title: A singular version of Leighton's comparison theorem for forced quasilinear second order differential equations (English)
Author: Došlý, Ondřej
Author: Jaroš, Jaroslav
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 39
Issue: 4
Year: 2003
Pages: 335-345
Summary lang: English
Category: math
Summary: We extend the classical Leighton comparison theorem to a class of quasilinear forced second order differential equations \[ (r(t)|x^{\prime }|^{\alpha -2}x^{\prime })^{\prime }+c(t)|x|^{\beta -2}x=f(t)\,,\quad 1<\alpha \le \beta ,\ t\in I=(a,b)\,, \qquad \mathrm {(*)}\] where the endpoints $a$, $b$ of the interval $I$ are allowed to be singular. Some applications of this statement in the oscillation theory of (*) are suggested. (English)
Keyword: Picone’s identity
Keyword: forced quasilinear equation
Keyword: principal solution
MSC: 34C10
idZBL: Zbl 1116.34316
idMR: MR2032106
Date available: 2008-06-06T22:42:34Z
Last updated: 2012-05-10
Stable URL:
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