Oscillatory Behavior of Quasilinear Neutral Delay Dynamic Equations on Time Scales

By means of the averaging technique and the generalized Riccati transformation technique, we establish some oscillation criteria for the second-order quasilinear neutral delay dynamic equations r t |xΔ t |γ−1xΔ t Δ q1 t |y δ1 t |α−1y δ1 t q2 t |y δ2 t |β−1y δ2 t 0, t ∈ t0,∞ T, where x t y t p t y τ t , and the time scale interval is t0,∞ T : t0,∞ ∩ T. Our results in this paper not only extend the results given by Agarwal et al. 2005 but also unify the oscillation of the second-order neutral delay differential equations and the second-order neutral delay difference equations.