Oscillation Results for Second-Order Neutral Functional Differential Equations

In this article, we obtain several comparison theorems for the second-order neutral differential equation $\frac{d}{dt}\left(r\right(t\left){\left(\frac{d}{dt}z\right(t\left)\right)}^{\gamma }\right)+q_1\left(t\right)x^{\lambda }\left(\sigma \right(t\left)\right)+q_2\left(t\right)x^{\beta }\left(\eta \right(t\left)\right)=0$, t ⩾ t ₀, where γ, λ, β are ratios of positive odd integers. We compare above equation with the first-order differential inequalities in the sense that the absence of the eventually positive solutions of these first-order inequalities implies the oscillation of the studied equation. (paper)