一类非线性差分方程的全局吸引性

Global Attractivity of a Nonlinear Difference Equation

研究了下列差分方程的动力学性质yn+1=pqyynn++yynn--kk,n=0,1,2,…,其中p,q∈[0,+∞),k是大于1的正整数,初值y-k,…,y-1为非负数,y0为一正实数.研究了上述方程所有正解的全局渐进稳定性,部分地解决了M.R.S.Kulenovic和G.La-das提出的公开问题.

Our aim in this paper is to investigate the dynamics of difference equation yn+1=pyn+yn-kqyn+yn-k,n=0,1,2,…,where p,q∈[0,+∞),k>1 is a positive integer and the initial conditions y-k,…,y-1 are non-negative and y0 is a positive real number.We show that the unique positive equilibrium of the equation is a global attractor.In particular,our results partly solve the open problem introduced by M.R.S.Kulenovic and G.Ladas.