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


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

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