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

V. Ganesan     (Aringar Anna Government Arts College, Namakkal, Tamilnadu, India)
Marappan Sathish Kumar     (Paavai Engineering College, Pachal, Namakkal, Tamilnadu, India)

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.

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References


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.




DOI: http://dx.doi.org/10.15826/umj.2017.2.013

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