Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation

The main purpose of this study is to establish new improved conditions for testing the oscillation of solutions of second-order neutral differential equation (r (l) (u' (l))gamma)' + q (l)x(beta) (sigma (l)) = 0, where l >= l(0) and u (l) = x (l) + px (rho(l)). By optimizing the commonly used relationship x > (1 - p)u, we obtain new criteria that give sharper results for oscillation than the previous related results. Moreover, we obtain criteria of an iterative nature. Our new results are illustrated by an example.