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 |
| _version_ | 1797830665807331328 |
|---|---|
| author | Said Grace John Graef Saroj Panigrahi Ercan Tunç |
| author_facet | Said Grace John Graef Saroj Panigrahi Ercan Tunç |
| author_sort | Said Grace |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T13:40:45Z |
| format | Article |
| id | doaj.art-a5b9759558664ed8a61424b8a05d2a7f |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:40:45Z |
| publishDate | 2012-12-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-a5b9759558664ed8a61424b8a05d2a7f2023-05-09T07:53:02ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752012-12-0120129611210.14232/ejqtde.2012.1.961953On the oscillatory behavior of even order neutral delay dynamic equations on time-scalesSaid Grace0John Graef1Saroj Panigrahi2Ercan Tunç3Cairo University, Orman, Giza, EgyptUniversity of Tennessee at Chattanooga, Chattanooga, TN, U.S.A.University of Hyderabad, Hyderabad-500046Gaziosmanpasa University, Tokat, TurkeyWe 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.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1953oscillationneutral delay equationstime scalehigher ordereven order |
| spellingShingle | Said Grace John Graef Saroj Panigrahi Ercan Tunç On the oscillatory behavior of even order neutral delay dynamic equations on time-scales Electronic Journal of Qualitative Theory of Differential Equations oscillation neutral delay equations time scale higher order even order |
| title | On the oscillatory behavior of even order neutral delay dynamic equations on time-scales |
| title_full | On the oscillatory behavior of even order neutral delay dynamic equations on time-scales |
| title_fullStr | On the oscillatory behavior of even order neutral delay dynamic equations on time-scales |
| title_full_unstemmed | On the oscillatory behavior of even order neutral delay dynamic equations on time-scales |
| title_short | On the oscillatory behavior of even order neutral delay dynamic equations on time-scales |
| title_sort | on the oscillatory behavior of even order neutral delay dynamic equations on time scales |
| topic | oscillation neutral delay equations time scale higher order even order |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=1953 |
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