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Title: Integral averages and oscillation of second order sublinear differential equations (English)
Author: Manojlović, Jelena V.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 55
Issue: 1
Year: 2005
Pages: 41-60
Summary lang: English
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Category: math
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Summary: New oscillation criteria are given for the second order sublinear differential equation \[ [a(t)\psi (x(t))x^{\prime }(t)]^{\prime }+q(t)f(x(t))=0, \quad t\ge t_0>0, \] where $a\in C^1([t_0,\infty ))$ is a nonnegative function, $\psi , f\in C({\mathbb R})$ with $\psi (x)\ne 0$, $xf(x)/\psi (x)>0$ for $x\ne 0$, $\psi $, $f$ have continuous derivative on ${\mathbb R}\setminus \lbrace 0\rbrace $ with $[f(x)/\psi (x)]^{\prime }\ge 0$ for $x\ne 0$ and $q\in C([t_0,\infty ))$ has no restriction on its sign. This oscillation criteria involve integral averages of the coefficients $q$ and $a$ and extend known oscillation criteria for the equation $x^{\prime \prime }(t)+q(t)x(t)=0$. (English)
Keyword: oscillation
Keyword: sublinear differential equation
Keyword: integral averages
MSC: 34C10
MSC: 34C15
MSC: 34C29
idZBL: Zbl 1081.34032
idMR: MR2121655
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Date available: 2009-09-24T11:20:46Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/127958
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