中立型时滞差分方程有界正解的存在性

ON EXISTENCE OF POSITIVE SOLUTIONS OF NEUTRAL DIFFERENCE EQUATION

本文我们考察了中立型的滞差分方程Δ（ｘｎ－ｘｎ－ｋ）＋Ｐｎｘｎ－ｌ＝０ｎ＝０，１，２，…（＊）其中Ｐｎ（ｎ＝０，１，２，…）是正实数，ｋ和ｌ是非负整数．我们证明了：当且仅当则差分方程（＊）存在有界正解．

In this paper, we consider the neutral delay difference equation Δ(xn-xn-k)+pnxn-1=0 n=0,1,2,3,… (*)where pn (n=0, 1, 2, …) are real numbers with pn≥0, k and l are nonnegative integers, We show that if and only ifthen Eq. (* ) has a positive solution.