概周期系数二维线性方程组特征数的估计  

The Estimates for Characteristic Numbers of Two Dimensional Linear Differential Equation with Almost Periodic Coefficients

作　　者：史金麟[1] 陈纪阳[2] 

机构地区：[1]福州大学数学系 [2]闽江学院数学系,福州350005

出　　处：《数学学报（中文版）》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)

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.

关 键 词：概周期系数 二维线性系 特征数 

分 类 号：O175.1[理学—数学]