# Oscillation of third-order quasilinear neutral dynamic equations on time scales with distributed deviating arguments

Volume 17, Issue 1, pp 41-52
Publication Date: March 15, 2017 Submission Date: April 20, 2016
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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.

### Share and Cite

##### 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.

•  34K11
•  34C11

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