New oscillation criteria for third order nonlinear functional differential equations
The authors consider the general third order functional differential equation \begin{align*} \left(a_{2}(\nu)\left[\left(a_{1}(\nu)\left(x'(\nu)\right)^{\alpha_{1}}\right)'\right]^{\alpha_{2}}\right)'+q(\nu) x^{\beta}(\tau(\nu))=0,\qquad\nu\geq \nu_{0}, \end{alig...
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| Format: | Article |
| Language: | English |
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University of Szeged
2024-12-01
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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=11204 |
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| _version_ | 1841533470218649600 |
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| author | John Graef Said Grace Gokula Chhatria |
| author_facet | John Graef Said Grace Gokula Chhatria |
| author_sort | John Graef |
| collection | DOAJ |
| description | The authors consider the general third order functional differential equation
\begin{align*}
\left(a_{2}(\nu)\left[\left(a_{1}(\nu)\left(x'(\nu)\right)^{\alpha_{1}}\right)'\right]^{\alpha_{2}}\right)'+q(\nu) x^{\beta}(\tau(\nu))=0,\qquad\nu\geq \nu_{0},
\end{align*}
and obtain sufficient conditions for the oscillation of all solutions.
It is important to note that $\alpha_{i}$ for $i=1,2$, and $\beta$ are somewhat independent of each other. The results obtained are illustrated with examples. |
| format | Article |
| id | doaj-art-2212ee3e661f485382e8b48ad0a8f81d |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-2212ee3e661f485382e8b48ad0a8f81d2025-01-15T21:24:59ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-12-0120247011110.14232/ejqtde.2024.1.7011204New oscillation criteria for third order nonlinear functional differential equationsJohn Graef0https://orcid.org/0000-0002-8149-4633Said Gracehttps://orcid.org/0000-0001-8783-5227Gokula Chhatria1https://orcid.org/0000-0002-2092-6420University of Tennessee at Chattanooga, Chattanooga, TN, U.S.A.Department of Engineering Mathematics, Cairo University, Orman, Giza, EgyptThe authors consider the general third order functional differential equation \begin{align*} \left(a_{2}(\nu)\left[\left(a_{1}(\nu)\left(x'(\nu)\right)^{\alpha_{1}}\right)'\right]^{\alpha_{2}}\right)'+q(\nu) x^{\beta}(\tau(\nu))=0,\qquad\nu\geq \nu_{0}, \end{align*} and obtain sufficient conditions for the oscillation of all solutions. It is important to note that $\alpha_{i}$ for $i=1,2$, and $\beta$ are somewhat independent of each other. The results obtained are illustrated with examples.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11204oscillationnonoscillationdelay differential equationcomparison method |
| spellingShingle | John Graef Said Grace Gokula Chhatria New oscillation criteria for third order nonlinear functional differential equations Electronic Journal of Qualitative Theory of Differential Equations oscillation nonoscillation delay differential equation comparison method |
| title | New oscillation criteria for third order nonlinear functional differential equations |
| title_full | New oscillation criteria for third order nonlinear functional differential equations |
| title_fullStr | New oscillation criteria for third order nonlinear functional differential equations |
| title_full_unstemmed | New oscillation criteria for third order nonlinear functional differential equations |
| title_short | New oscillation criteria for third order nonlinear functional differential equations |
| title_sort | new oscillation criteria for third order nonlinear functional differential equations |
| topic | oscillation nonoscillation delay differential equation comparison method |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11204 |
| work_keys_str_mv | AT johngraef newoscillationcriteriaforthirdordernonlinearfunctionaldifferentialequations AT saidgrace newoscillationcriteriaforthirdordernonlinearfunctionaldifferentialequations AT gokulachhatria newoscillationcriteriaforthirdordernonlinearfunctionaldifferentialequations |