一类非线性时滞差分方程的有界持久性

Boundedness and Persistence of the Delay Difference

考虑一类非线性时滞差分方程: 这里p0,p1,…,pk,Ak均为正常数,A0,A1,…,Ak-1均为非负常数,初始值x-k,x-k+1,…,x0为任意给定的正数。利用分析的技巧,得到了方程的正解有界持久的某些充分条件,部分回答了G．Ladas提出的一个公开问题;改进了已有文献中的相关工作。

In this paper, we consider the following equation xn＋1=∑i=0 ^k Ai/xn-i^pi,n=0,1,2,3… Where p0 , p1 , ..., pk , At are positive numbers, A0, A1, ..., Ak-1 are not negative numbers,and the initial values x-k, x-k＋1, x0 are arbitrary positive numbers.A sufficient condition for boundedness and persistence of positive solutions is obtained. A conjecture by G.Ladas is partially proved here, and the results of some known paperI improved.