一类有理差分方程的全局渐近稳定性

研究差分方程xn＋1=fgh＋f＋g＋h＋a/fg＋gh＋hf＋1＋a（n=0，1，…）的全局渐近稳定性，其中a∈（1,＋∞）,f=f（x-r1,…，x-rk）∈C（（0,＋∞）^k,（0,＋∞））,g=g（xn-m1,…,xn-ml）∈C（（0,＋∞）^l,（0,＋∞））,h=h（xn-s1,…,xn-sσ）∈C（（0,＋∞）^σ,（0,＋∞））,k,lσ∈{1,2,…},0≤r1〈…〈rk，0≤m1〈…〈ml，0≤s1〈…〈sσ，并且初值为正实数．给出了该方程关于唯一正平衡点=↑x=1的全局稳定的充分条件，推广了参考文献5]-7]中的一些结果．

Global Asymptotic Stability of a Class of Rational Difference Equation

We study global asymptotic for positive solutions to the equation xn＋1=fgh＋f＋g＋h＋a/fg＋gh＋hf＋1＋a（n=0,1,…）,where a∈（1,＋∞）,f=f（x-r1,…,x-rk）∈C（（0,＋∞）^k,（0,＋∞））,g=g（xn-m1,…,xn-ml）∈C（（0,＋∞）^l,（0,＋∞））,h=h（xn-s1,…,xn-sσ）∈C（（0,＋∞）^σ,（0,＋∞））,with k,l,σ∈{1,2,…},0≤r1〈…〈rk,0≤m1〈…〈ml,0≤s1〈…〈sσ and the initial values are positive real numbers. Thesufficient conditions is given under which the unique equilibrium =↑x=1 = 1 of this equation is globally asymptotic stable, which inproves and the corresponding results obtained in the literature 5]-7].