### ON THE OSCILLATION OF A THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH NEUTRAL TYPE

#### Abstract

In this article, we investigate that oscillation behavior of the solutions of the third-order nonlinear differential equation with neural type of the form

$$

\Big(a_{1}(t)\big(a_{2}(t)Z^{\prime}(t)\big)^{\prime}\Big)^{\prime}

+ q(t) f\big(x(\sigma(t))\big) = 0, \quad t\geq t_0 > 0,

$$

where \(Z(t) := x(t)+p(t)x^{\alpha}(\tau(t))\). Some new oscillation results are presented that extend those results given in the literature.

#### Keywords

Oscillation, Non-linear, Neutral differential equation, Third order.

#### Full Text:

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- Agarwal R.P., Bohner M., Li T., Zhang C. Oscillation of second-order Emden–Fowler neutral delay differential equations // Ann. Math. Pura Appl., 2004. Vol. 193, no. 6. P. 1861–1875. DOI: 10.1007/s10231-013-0361-7
- Agarwal R.P., Bohner M., Li T., Zhang C. A new approach in the study of oscillatory behavior of even-order neutral delay differential equations // Appl. Math. Comput., 2013. Vol. 225. P. 787–794. DOI: 10.1016/j.amc.2013.09.037
- Dix J.G. Oscillation of solutions to a neutral differential equation involving an n-order operator with variable coefficients and a forcing term // Differ. Equ. Dyn. Syst., 2014. Vol. 22, no. 1. P. 15–31. DOI: 10.1007/s12591-013-0160-z
- Ganesan V. and M. Sathish Kumar Oscillation criteria for second-order neutral differential equations // Int. J. of Pure and Appl. Math., 2017. Vol. 113, no. 12. P. 151–159.
- Ganesan V. and M. Sathish Kumar Oscillation of certain third order nonlinear differential equation with neutral terms // Bangmod Int. J. of Math. Comp. Sci., 2017. Vol. 3, no. 1–2. P. 53–60.
- Ganesan V. and M. Sathish Kumar Oscillation theorems for third-order retarded differential equations with a sublinear neutral term // Int. J. of Pure and Appl. Math., 2017. Vol. 114, no. 5, P. 63–70.
- Graef J.R., Savithri R. and Thandapani E. Oscillatory properties of third order neutral delay differential equations // Discrete and Continuous Dynamical Systems A, 2003. P. 342–350.
- Thandapani E. and Li T. On the oscillation of third-order quasi-linear neutral functional differential equations // Archivum Mathematicum, 2011. Vol. 47. P. 181–199.
- Tamilvanan S., Thandapani E., Džurina J. Oscillation of second order nonlinear differential equation with sublinear neutral term // Differential Equations and Applications, 2016. Vol. 9, no. 1. P. 29–35. DOI: 10.7153/dea-09-03
- Baculíková B. and Džurina J. Oscillation of third-order neutral differential equations // Math. Comput. Modelling, 2010. Vol. 52. P. 215–226. DOI: 10.1016/j.mcm.2010.02.011
- Candan T., Dahiya R.S. Oscillation of third order functional differential equations with delay // Electron. J. Diff. Eqns. Conference, 2003. Vol. 10. P. 79–88.
- Candan T., Dahiya R.S. Functional differential equations of third order // Electron. J. Diff. Eqns. Conference, 2005. Vol. 12. P. 47–56.
- Lin X. and Tang X. Oscillation of solutions of neutral differential equations with a superlinear neutral term // Applied Mathematics Letters, 2007. Vol. 20. P. 1016–1022. DOI: 10.1016/j.aml.2006.11.006
- Agarwal R.P., Bohner M., Li T. and Zhang C. Oscillation of second order differential equations with a sublinear neutral term // Carpathian J. Math, 2014. Vol. 30. P. 1–6.

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