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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1417-3875 |