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.