摘要
研究了形如Ｅｘ（ｋ）＝Ａｘ（ｋ）＋ｆ（ｋ，Ｘ（ｋ））的非线性差分方程解的极限性质．Ｅｘ（ｋ）＝ｘ（ｋ＋１）．Ａ是ｎ×ｎ（ｎ≥２）阶常数矩阵．ｘ（ｋ）∈Ｒｎ．ｆ：Ｊ×Ｇ→Ｒｎ，Ｊ＝｛ｊ０＋ｋ｜ｋ＝１，２，…．ｊ０∈Ｒ｝，Ｇ．Ｒｎ．ｆ满足对任一紧集中的ｘ（ｋ）一致有ｆ（ｋ，ｘ（ｋ））→０，当ｋ→∞．利用差分不等式及比较原理得到：当Ａ的谱半径小于１时，方程的有界解均趋于零解．当Ａ的话半径大于１时，方程有无界解．并研究了所有解均趋于零解的充分条件．
A study is presented of n-dimensional diffevence equation: Ex(k) =Ax(k) +f(k,x (k)).Ex(k) =x(k+1 ), x(k) ∈ Rn, A is a n×n matrix of constant, f(k,x(k) ):J×G→Rn,map f satisfied with: as k→∞, f(k,x(k)) uniformly approaches zero for every x(k) in any compact set. Based on comparison theorem and certain difference inequalities,it can be obtained that: when spectral radius of matrix A is less than 1, the bounded solutions of equation tend to zero; when spectral radius of matrix A is more than 1,the difference equation have boundless solutions. Finally,a sufficient condition for all solutions tending to zero can be obtained.
出处
《陕西师大学报（自然科学版）》
CSCD
1995年第4期6-8,共3页
Journal of Shaanxi Normal University(Natural Science Edition)
关键词
渐近方程
极限集
有界解
非线性
差分方程
asymptotic equation
spectral radius
limits set
bounded solution
