| 概周期系数二维线性方程组特征数的估计 |
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| 引用本文： | 史金麟,陈纪阳.概周期系数二维线性方程组特征数的估计[J].数学学报,2005,48(3):519-526. |
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| 作者姓名： | 史金麟 陈纪阳 |
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| 作者单位： | 福州大学数学系，闽江学院数学系 福州350002闽江学院数学系福州，350005，福州350005 |
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| 基金项目： | 福建省教育厅科技资助项目(JA03014) |
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| 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.
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| 关 键 词： | 概周期系数 二维线性系 特征数 |
The Estimates for Characteristic Numbers of Two Dimensional Linear Differential Equation with Almost Periodic Coefficients |
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| Jin Lin SHI.The Estimates for Characteristic Numbers of Two Dimensional Linear Differential Equation with Almost Periodic Coefficients[J].Acta Mathematica Sinica,2005,48(3):519-526. |
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| Authors: | Jin Lin SHI |
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| Institution: | Jin Lin SHI Department of Mathematics, Fuzhou University, Fuzhou 350002, P. R. China Department of Mathematics, College of Minjiang, Fuzhou 350005, P. R. China Ji Yang CHEN Department of Mathematics, College of Minjiang, Fuzhou 350005, P. R. China |
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| Abstract: | 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. |
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| Keywords: | Almost periodic coefficients Two dimensional linear system Characteristic number |
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