一类中立型差分方程的振动性及其正解的存在性

Oscillation and Existence of Positive Solution for a Neutral Difference Equations

研究了中立型差分方程Δ（ｘｎ－ｐｎｘｎ－ｋ）＋∑ｍｉ＝１ｐｉｎｘｎ－ｌｉ＝０（＊）解的振动性及其正解的存在性。其中｛ｐｎ｝，｛ｐｉｎ｝（ｉ＝１，２，…，ｍ）是非负实数列，并且０≤ｐｎ≤１（ｎ＝０，１，２，…），ｋ，ｌ１，ｌ２，…ｌｍ是非负整数。在适当的条件下，建立了这类方程（＊）振动及其具有正解的充分条件。

In this paper,we investigated a neutral difference equationsΔ(xn-pnxn-k)+∑mi=1pinxn-li=0(*)Where {pn},{pin}(i=1,2,…,m) are nonnegative real numbers sequences with 0≤pn≤1(n=0,1,2,…),k,l1,l2,…lm are nonnegative cntegers.Under appropriate conditions.We established sufficient conditions for the oscillation and existence of positive solutions of equations (*).