Oscillation of third-order quasilinear neutral dynamic equations on time scales with distributed deviating arguments
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Authors
M. Tamer Senel
- Department of Mathematics, Faculty of Sciences, Erciyes University, 38039, Kayseri, Turkey.
Nadide Utku
- Institute of Sciences, Erciyes University, 38039, Kayseri, Turkey.
Abstract
The aim of this paper is to give oscillation criteria for the third-order quasilinear neutral delay dynamic equation \begin{equation*}
\bigg[r(t)\big([x(t)+p(t)x(\tau_{0}(t))]^{\Delta\Delta}\big)^{\gamma}\bigg]^{\Delta}+\int_{c}^{d}q_{1}(t)x^{\alpha}(\tau_{1}(t,\xi))\Delta\xi+\int_{c}^{d}q_{2}(t)x^{\beta}(\tau_{2}(t,\xi))\Delta\xi=0,
\end{equation*}
on a time scale \(\mathbb{T}\), where \(0<\alpha<\gamma<\beta\). By using a generalized Riccati transformation and integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.
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ISRP Style
M. Tamer Senel, Nadide Utku, Oscillation of third-order quasilinear neutral dynamic equations on time scales with distributed deviating arguments, Journal of Mathematics and Computer Science, 17 (2017), no. 1, 41-52
AMA Style
Senel M. Tamer, Utku Nadide, Oscillation of third-order quasilinear neutral dynamic equations on time scales with distributed deviating arguments. J Math Comput SCI-JM. (2017); 17(1):41-52
Chicago/Turabian Style
Senel, M. Tamer, Utku, Nadide. "Oscillation of third-order quasilinear neutral dynamic equations on time scales with distributed deviating arguments." Journal of Mathematics and Computer Science, 17, no. 1 (2017): 41-52
Keywords
- Oscillation
- third order quasilinear neutral dynamic equation with distributed deviating arguments
- time scales.
MSC
References
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