差分方程解的稳定性、有界性及概周期解的存在性  

Stability and Boundedness of Solutions and Existence of Almost Periodic Solution for Difference Equations

作　　者：杨喜陶[1] 

机构地区：[1]湖南科技大学数学系,湘潭411201

出　　处：《数学物理学报（A辑）》2008年第5期870-878,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(10671021);湖南科技大学博士基金(E50642);中南大学博士后基金资助

摘　　要：作者通过Liapunov泛函建立了一类高维差分方程解一致稳定、一致渐近稳定及指数渐近稳定的充要条件.此外,作者还证明了解的一致渐近稳定性蕴含解的有界性,同时也给出了概周期差分方程存在概周期解的一个充分条件.By using Liapunov function, the author establishes sufficient and necessary conditions for the uniform stability, uniformly asymptotic stability and exponential stability of solutions for a high dimension difference equation. Moreover, the author also proves that the uniformly asymptotic stability implies the boundedness of solutions. A sufficient condition is given for the existence and uniformly asymptotic stability of almost periodic solutions for almost periodic difference equations.

关 键 词：差分方程 稳定性 有界性 概周期 LIAPUNOV泛函 

分 类 号：O175.14[理学—数学]