【摘要】 研究具有可变时滞的高阶非自治中立型差分方程△^m(X_n-cx_n-k)+h(n,x_n-ln)=0 （n=0,1,2,...）的振动性．利用Banach空间的压缩映象原理,得到了这类差分方程振动的必要条件．利用偏序集中的Knaster不动点定理,得到了这类方程振动的充分必要条件．同时得到了这类差分方程存在最终正解的准则．更多还原

【Abstract】 This paper is concerned with the oscillation of high order neutral type delay difference equationsΔ^m(x_n-cx_n-k)+h(n,x_（n-1）n)=0,n=0,1,2,....By the principle of con- traction mapping in Banach space and the principle of Knaster fixed point in partial order set, the necessary and sufficient conditions of oscillation of these equations are obtained.At the same time,the existence criterion of eventually positive solutions of these equations is presented.更多还原