非线性差分方程的全局吸引性  

Global Attractivity for a Nonlinear Difference Equation

作　　者：王英[1] 

机构地区：[1]邵阳师范高等专科学校数学系,湖南邵阳422000

出　　处：《西南师范大学学报（自然科学版）》2001年第6期640-644,共5页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：研究了差分方程xn+ 1-xn+Pnf(xn-k) =0n∈N (1)的渐近性态 ,得出了方程零解全局吸引的充分条件 .定理　设 f为不减函数 ,且当x≠ 0时 ,｜f(x)｜<｜x｜ ,∑∞n =0Pn =∞ .若∑ni=n-kPi ≤ β=32 +12 (k +1) 　　 n∈N(n0 )成立 ,那么方程 (1)的零解是全局吸引的 .The asymptotic behavior of difference equation x\-\{n+1\}-x\-n+P\-nf(x\-\{n-k\})=0 n∈N(1)is discussed. Sufficient conditions for the global allvactivity of the zero solution are obtained. Theorem Assume that f is a nondecresing function, ｜f(x)｜<｜x｜ for every ≠0, ∑∞n=0P\-n=∞ and∑ni=n-kP\-i≤β=32+12(k+1)\ \ n∈N(n 0)Then the zero solution of equation (1) is global attractivity.

关 键 词：全局吸引性 振动性 零解 非线性自治差分方程 渐近性态 非振动解 

分 类 号：O241.3[理学—计算数学]