New Oscillation Conditions Test for Neutral Differential Equations

Abstract

In this work, we investigate new oscillation conditions of delay differential equations of second-order. We start by finding new relations  and inequalities between the corresponding function and its solution, also with its derivatives. The new inequalities allow us to improve the asymptotic and oscillation conditions of the solutions of the this equation. By using an improved method and approach, we obtain new criteria that test the all solutions oscillation. The article provides some examples that highlight the significance of new conditions and properties.