多滞量非线性偏差分方程的渐近稳定性

Asymptotic stability of more delays nonlinear partial difference equation

研究一类多滞量偏差分方程xm+1,n+axm,n+1=1+(xm-k,n-blxm-2k,n-2l)p,m,n=0,1,2,…,其中:i)a,b∈(0,+∞),k,l,p∈N+={1,2,…};ii){xm,n}满足初始条件:xm,n=m,n>0,对每个(m,n)∈Ω0,Ω0={(m,n)|m≥-2k,n≥-2l}\{(m,n)|m≥1,n≥0}.首先建立了其解的持久性和振动性的充分条件,并将方程的解与引理2中的收敛数列进行比较,利用数学归纳法证明了解的一致渐近稳定性。

Consider partial difference equation xm＋1,a＋axm,n＋1=b/1＋（xm-k,n-lxm-2k,n-21）^p,m,n=0,1,2…,where：i）1,b∈（0,＋∞）,k,l,P∈n^＋={1,2,…｜;ii）｜xm,n｜satisfies xm,n=Φm,n〉0,for all（m,n）∈Ω0,Ω0=（m,n）｜m≥-2k,n∈-2l｜／｜（m,n）｜m≥1,n≥0｜. Firstly, the sufficient conditions of the permanence and oscillation of the solutions are established. Next, the solutions of the partial difference equation are compared with the convergent sequences of lemma 2. By means of mathematical induction method, unform asymptotic stability of the solutions of the partial difference equation is obtained.