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Title: On property (B) of higher order delay differential equations (English)
Author: Baculíková, Blanka
Author: Džurina, Jozef
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 48
Issue: 4
Year: 2012
Pages: 301-309
Summary lang: English
Category: math
Summary: In this paper we offer criteria for property (B) and additional asymptotic behavior of solutions of the $n$-th order delay differential equations \begin{equation*} \big (r(t)\big [x^{(n-1)}(t)\big ]^{\gamma }\big )^{\prime }=q(t)f\big (x(\tau (t))\big )\,. \end{equation*} Obtained results essentially use new comparison theorems, that permit to reduce the problem of the oscillation of the n-th order equation to the the oscillation of a set of certain the first order equations. So that established comparison principles essentially simplify the examination of studied equations. Both cases $\int ^{\infty } r^{-1/\gamma }(t)\,{t}=\infty $ and $\int ^{\infty } r^{-1/\gamma }(t)\,{t}<\infty $ are discussed. (English)
Keyword: $n$-th order differential equations
Keyword: comparison theorem
Keyword: oscillation
Keyword: property (B)
MSC: 34C10
MSC: 34K11
idMR: MR3007612
DOI: 10.5817/AM2012-4-301
Date available: 2012-12-17T13:54:45Z
Last updated: 2013-09-19
Stable URL:
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