On the oscillatory behavior of even order neutral delay dynamic equations on time-scales
We establish some new criteria for the oscillation of the even order neutral dynamic equation \begin{equation*} \left( a(t)\left( \left( x(t)-p(t)x(\tau (t))\right) ^{\Delta^{n-1}}\right) ^{\alpha }\right) ^{\Delta }+q(t)\left( x^{\sigma}(g(t))\right) ^{\lambda }=0 \end{equation*} on a time scale $\...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2012-12-01
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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=1953 |
| Summary: | We establish some new criteria for the oscillation of the even order neutral dynamic equation
\begin{equation*}
\left( a(t)\left( \left( x(t)-p(t)x(\tau (t))\right) ^{\Delta^{n-1}}\right) ^{\alpha }\right) ^{\Delta }+q(t)\left( x^{\sigma}(g(t))\right) ^{\lambda }=0
\end{equation*}
on a time scale $\mathbb{T}$, where $n \geq 2$ is even, $\alpha $ and $\lambda $ are ratios of odd positive integers, $a$, $p$ and $q$ are real valued positive rd-continuous functions defined on $\mathbb{T}$, and $g$ and $\tau $ are real valued rd-continuous functions on $\mathbb{T}$. Examples illustrating the results are included. |
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| ISSN: | 1417-3875 |