【摘要】 本文研究了一类具变时滞的非线性差分方程解的振动性，获得了该方程解的振动准则．将结论应用于差分方程ΔＸｎ ＋ ｐｎｘｎ－ ｋｎ ＝ ０　　ｎ ＝ ０，１，２，… （）其中ｐｎ≥０，｛ｋｎ｝是正整数数列且ｌｉｍｎ→∞｛ｎ－ ｋｎ｝＝ ∞．我们得到了方程（）振动的新的充分条件．更多还原

【Abstract】 In this paper,the oscillation of all solutions of the following variable delay difference equation:ΔX n+∑mi=1p i,n f i(x n-k i,1,n ,…,x n-k i,m i,n +h(n,x n-k 1,n ,…,x n-l,n )=0, n=0,1,2,…are investigated,Under approriate hypotheses,criteria for the oscillations of all solutions of difference equation are obtained.We also obtained some new sufficient conditions for the oscillation of all solutions of the following difference equation:ΔX n+p nx n-k n =0, n=0,1,2,…where p n≥0,{k n} is a sequence of positive integers satisfying lim n→∞(n-k n)=∞ .更多还原