一类差分方程解的全局性分析

Global Analysis of Solutions of the Difference Equations

研究差分方程xn+1=βxn+∑pi=1γixn-i/A+Bxn+∑qn=0,1,Cjxn-jn=0,1,…的全局性质,其中A,B,β∈(0,+∞),p,q∈N+={1,2,…},α=max{p,q},γ1,γ2,…,γp,C1,C2,…,Cq∈[0,1],满足∑i=1γi=∑j=1Cj=1,初始值x0,x-1,…,x-α∈(0,∞).得到该方程的每个正解收敛于平衡解的若干充分条件.

We study global behavior of the following difference equationxn＋1=βxn＋∑pi=1γixn-iA＋Bxn＋∑qj=1Cjxn-j,n=0,1,…,where A,B,β∈（0,＋∞）,p,q∈N＋={1,2,…},α=max{p,q},γ1,γ2,…,γp,C1,C2,…,Cq∈,with ∑pi=1γi=∑qj=1Cj=1,and the initiual conditions x0,x-1,…,x-α∈（0,∞）.We give sufficient conditions under which every solution of this equation converges to the equliibrium solution.