Order Quasilinear Neutral Differential Equation Of Vibration,

This paper is divided into three parts. In the first part, introduce the generalsituation on this area and the main work about this article. In the sceond part,by using Riccati transformation and averaging technique, some sufficient conditionsare obtained for oscillation of the second-order quasilinear neutral delay differenceequation△[r_n|△z_n|^α-1△z_n]+q_nf(x_n-σ)=0, (E)under the condition sum from n=0 to∞1／r_n^1／α=∞. These criteria obtained here extend and includesome results due to Cheng, Li and Yeh, Luo. In the third part, by using Riccatitransformation and mathematical analytic methods, we also obtain some sufficientconditions for oscillation of the equation (E) under the condition sum from n=0 to∞1／r_n^1／α＜∞.Theresults obtained here extend and enrich some work of [25-27]. So far, we have discussedthe oscillation criteria of equation (E) fully.