【摘要】 本文研究一类二阶有理差分方程xn+1=(α+βxn)/(A+Bxn+Cxn-1)n=0,1,...的正解的全局渐近稳定性,这里的α,β,A,B,C∈(0,∞),初始条件x-1,x0是非负实数.利用极限理论研究了该方程的不变区间及其性质,证明了该类差分方程的平衡点是全局渐近稳定的,从而解决了文献[5]中的一个猜想:该方程的所有正解有有限极限.更多还原

【Abstract】 This paper discusses the global asymptotic stability of positive solutions in the following second order rational difference equation:xn+1=(α+βxn)/(A+Bxn+Cxn-1)n=0,1,... where the parameters α,β,A,B,C∈(0,∞), and the initial values x-1,x0 are non-negative real numbers.By using the theory of limit,we study the invariant interval and characters of this equation,and prove that equilibrium point in this kind of difference equation is globally asymptotic stable,which further solves a conjecture in the literature[5]:all the positive solutions of the above equation has a finite limit.更多还原