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中文摘要：
研究差分方程xn＋1=α＋β,xn/α＋αnxn＋…＋αkxn-k,n=0,1…的全局渐进稳定性，其中参数α，β，α，αi∈（0，∞），i=0，1，…，k，x-k，…x-1∈（0，∞）和x0∈（0，∞）．证明了唯一正平衡点是全局稳定性的当且仅当它是局部渐进的．
英文摘要：
The global asymptotic stability of the difference equation xn＋1=α＋β,xn/α＋αnxn＋…＋αkxn-k is studied,n = 0,1…where the parameters α,β,α,αi∈（0,∞）for i=0,1,…,k,x-k,…x-1∈（0,∞）and x0∈（0,∞）. It is proved that the unique positive equilibrium is globally asymptotically stable only if it is locally asymptotically.
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