In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, xn+ 1=xn+xn- 1xn- 2 +a xnxn- 1+xn- 2 +a, n =0 ,1 ,..., ...In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, xn+ 1=xn+xn- 1xn- 2 +a xnxn- 1+xn- 2 +a, n =0 ,1 ,..., where a∈ [0 ,∞ ) and the initial values x- 2 ,x- 1,x0 ∈ (0 ,∞ ) .As a special case,a conjecture by Ladas is confirmed.展开更多
In this paper, a sufficient condition for boundedness and persistence of the solutions of the following delay difference equation is obtained. A conjecture by G.Ladas is proved herexn+1=A/xpn+B/xqn-1,\ n=0,1,…q, x-1,...In this paper, a sufficient condition for boundedness and persistence of the solutions of the following delay difference equation is obtained. A conjecture by G.Ladas is proved herexn+1=A/xpn+B/xqn-1,\ n=0,1,…q, x-1, x0∈(0,∞). Received June 2,1997. Revised September 15, 1997.1991 MR Subject Classification:39A10.展开更多
基金Supported by the National Natural Science Foundation of China(1 0 0 71 0 2 2 ) Mathematical TianyuanFoundation of China(TY1 0 0 2 6 0 0 2 - 0 1 - 0 5 - 0 3 ) Shanghai Priority Academic Discipline Foundation
文摘In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, xn+ 1=xn+xn- 1xn- 2 +a xnxn- 1+xn- 2 +a, n =0 ,1 ,..., where a∈ [0 ,∞ ) and the initial values x- 2 ,x- 1,x0 ∈ (0 ,∞ ) .As a special case,a conjecture by Ladas is confirmed.
文摘In this paper, a sufficient condition for boundedness and persistence of the solutions of the following delay difference equation is obtained. A conjecture by G.Ladas is proved herexn+1=A/xpn+B/xqn-1,\ n=0,1,…q, x-1, x0∈(0,∞). Received June 2,1997. Revised September 15, 1997.1991 MR Subject Classification:39A10.
