线性常微分方程组解的特征数的估计 |
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引用本文: | 王树禾,麦结华. 线性常微分方程组解的特征数的估计[J]. 数学学报, 1997, 40(6). DOI: cnki:ISSN:0583-1431.0.1997-06-015 |
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作者姓名: | 王树禾 麦结华 |
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作者单位: | 中国科学技术大学数学系,汕头大学数学研究所 |
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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.}
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关 键 词: | 特征数,差异性质,正常解组 |
收稿时间: | 1996-07-10 |
修稿时间: | 1997-02-17 |
Estimate of Characteristic Numbers of Linear Ordinary Differential Equations System |
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Affiliation: | Wang Shuhe(Department of Mathematics, University of Science and Technology of China, Hefei 230026, China; )Mai Jiehua(Institute of Mathematics, Shantou University, Shantou 515063, China)) |
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Abstract: | 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. |
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Keywords: | Characteristic number Diversity Canonical solution system |
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