Asymptotic and oscillatory behavior of higher order quasilinear delay differential equations
In the paper, we offer such generalization of a lemma due to Philos (and partially Staikos), that yields many applications in the oscillation theory. We present its disposal in the comparison theory and we establish new oscillation criteria for $n-$th order delay differential equation \begin{equati...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2012-11-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1807 |
| Summary: | In the paper, we offer such generalization of a lemma due to Philos (and partially Staikos), that yields many applications in the oscillation theory. We present its disposal in the comparison theory and we establish new oscillation criteria for $n-$th order delay differential equation
\begin{equation*}
\left(r(t)\left[x'(t)\right]^{\gamma}\right)^{(n-1)}+q(t)x^{\gamma}(\tau(t))=0.\tag{$E$}
\end{equation*}
The presented technique essentially simplifies the examination of the higher order differential equations. |
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| ISSN: | 1417-3875 |