概自守系统与回复系统的零解稳定性  

On the Stability of Zero Solution for Almost Automorphic and Recurrent Systems

作　　者：江良平[1] 

机构地区：[1]福州大学数学系,福州350002

出　　处：《应用数学》2002年第S1期12-15,共2页Mathematica Applicata

基　　金：福建省教育厅科研项目 (JB0 0 0 79)

摘　　要：方程x′=f(t,x)零解渐近稳定的经典判据是存在定正函数V ,而dV/dt定负 .前人已证当f(t,x)是概周期函数时dV/dt定负这一条件可减弱为dV/dt小于或等于 0 .本文将证明该结论对f(t,x)是概自守函数和回复函数时也成立 .The classical criterion of asymptotic stability of zero solution of equation x′=f(t,x)assumes existence of possitive definite function V and negative definite function dV/dt.If f(t,x) is almost periodic function the criterion can be weaken to the case in which dV/dt is not negative definite but is less than of equal to zero.In this paper,we extend the conclusion to almost automorphic function and recurrent function.

关 键 词：零解稳定性 概自守函数 回复函数 

分 类 号：O175.13[理学—数学]