Oscillation of solutions to third-order half-linear neutral differential equations

In this article, we study the oscillation of solutions to the third-order neutral differential equations $$ Big(a(t)ig([x(t)pm p(t)x(delta(t))]''ig)^alphaBig)' + q(t)x^alpha( au(t)) = 0. $$ Sufficient conditions are established so that every solution is either oscillatory or converges to zero. In particular, we extend the results obtain in [1] for $a(t)$ non-decreasing, to the non-increasing case.