摘要
复数域上线性系统x=A(t)x,当A(t)=(aij(t))n×n具有(n,N,r)差异性质且rn时,解的特征数j有估计λj-limt→∞1t∫tt0Reaj(τ)dτn-1r+1-nlimt→∞1t∫tt0A(τ)dτ,j=1,2,…,n,其中A(t)=max{|aij(t)|:i,j=1,2,…,n,i≠j.}
Let λ1,λ2,…,λn be characteristic numbers of linear differential equation system in complex field =A(t)x, t∈(0,∞), and A(t) =(aij(t))n×n has (n,N,r)diversity, rn, then λj -limt→∞ 1t∫tt0Reajj (τ)dτn-1r+1-nlimt→∞ 1t∫tt0A*(τ)dτ, where j=1,2,…,n, A* (t)=max{|aij (t)|: i,j=1,2,…,n, i≠j}, t00.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
1997年第6期901-912,共12页
Acta Mathematica Sinica:Chinese Series
关键词
特征数
正常解
线性
常微分方程组
解
估计
Characteristic number, Diversity, Canonical solution system