Oscillation Theorems for Second-order Neutral Functional Dynamic Equations on Time Scales

In this article, we obtain several comparison theorems for the second-order neutral dynamic equation “ r(t) ` [x(t) + p(t)x(τ(t))] ́γ”∆ + q1(t)x (δ(t)) + q2(t)x (η(t)) = 0, where γ, λ, β are ratios of positive odd integers. We compare such equation with the first-order dynamic inequalities in the sense that the absence of the eventually positive solutions of these first-order inequalities implies the oscillation of the studied equation.