一类二阶非线性差分方程的全局吸引性

Global attractivity in a second-order nonlinear difference equation

考虑二阶非线性差分方程xn+1=a+bxn/A+xn-1,n=0,1,2,….证明了当条件a,b,A∈(0,∞)成立时方程的唯一正平衡点=(b-A+((b-A)2+4a))～(1/2))/2是方程的所有正解的一个全局吸引子,所得推论证明了由Kocic和Ladas提出的一个猜想是正确的.

Considering second-order nonlinear difference equation xn＋1=a＋bxn/A＋xn-1,n=0,1,2,…,this paper proves that the unique positive equilibrium x^-=（b-A＋√（（b-A）2＋4a））～（1/2））/2 is a global attractor of all positive solutions of the equation.The obtained corollary proves a conjecture which is given by Kocic and Ladas.