方程Δx_n=γ_nx_n(1+λx_n)(1-x_n)的全局吸引性

Global Attractivity of the Equation Δx_n=γ_nx_n(1+λx_n)(1-x_n)

考虑非自治差分方程 Δxn=γnxn( 1 +λxn) ( 1 -xn) n =0 ,1 ,2… 的全局吸引性 ,这里 {γn}是正实数列 ,λ >0获得方程每一解趋于 1的充分条件 .

In this paper, we consider the nonautonomous difference equation\;\%Δx\-n=γ\-nx\-n(1+λx\-n)(1-x\-n)\ n=0,1,2,\:\% where {\%γ\-n\%} is a sequence of positive number, \%λ\%>0. We obtain some sufficient conditions for every positive solution of equation satisfying the initial condition to converge to 1 as \%n\%\?∞.