一类中立型差分方程正解的分类

THE CLASSIFICATION OF POSITIVE SOLUTIONS TO NEUTRAL DIFFERENCE EQUATIONS

考虑中立型差分方程△(xn-rn/r(n-k)*x(n-k))+qnx(n-l)=0 其中ｋ＞０，ｌ＞０，ｒｎ＞０，ｑｎ≥０．将（＊）的正解分为Ａ，Ｂ，Ｃ和Ｄ四种类型，且证明了有Ａ，Ｂ，Ｄ型正解的充要条件．

Consider a class of neutral difference equation of form△(xn-rn/r(n-k)*x(n-k))+qnx(n-l)=0 where k>0,l>0, rn>0, qn≥0. All positive solutions of (*) can be classified into four types, A, B, C, and D. Obtain sufficient and necessary conditions for the existence of A - type, B-type and D -type positive soluhons of (*).