摘要
常系数线性系(yx)'=(cdab)(yx)具有指数型二分性(特征根一正一负)的充要条件是ad-bc<0.本文说明概周期线性系(yx)'=(a(t)d(t)a(t)b(t))(yx)当a(t)d(t)-b(t)c(t)<0时,一般也有指数型二分性.同时给出特征数较准确的估计.
Autonomous linear equation (yx)'=(cd ab)(yx) has an exponential dichotomy (has a positive eigenvalue and a negative eigenvalue) if and only if ad-bc < 0. In this paper, we show that, if a(t)d(t) - b(t)c(t) < 0, almost periodic linear system ( yx ) = (c(t)d(t) a(t)b(t)) (yx) usually has an exponential dichotomy, and give relatively exact estimates for characteristic numbers.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2005年第3期519-526,共8页
Acta Mathematica Sinica：Chinese Series
基金
福建省教育厅科技资助项目(JA03014)
关键词
概周期系数
二维线性系
特征数
Almost periodic coefficients
Two dimensional linear system
Characteristic number
