OSCILLATION OF CERTAIN THIRD ORDER NONLINEAR DIFFERENTIAL EQUATION WITH NEUTRAL TERMS

Abstract

The main goal of this work is to establish some new comparison theorems for oscillation
of solutions to the third order nonlinear differential equations with neutral terms of the form\begin{equation}
\left[ r(t)\left[ \left( x(t)+ \sum_{i=1}^{n} p_{i}(t)x(\eta_{i}(t))\right)^{\prime\prime}\right] ^{\gamma }\right]^{\prime}
+ q(t) x^{\gamma}(\sigma(t)) = 0,
\end{equation}
are presented. We give several Theorems and related examples to illustrate the main results.