| 关于N阶混合型线性微分方程特征根的分布 |
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| 引用本文： | 袁俊华.关于N阶混合型线性微分方程特征根的分布[J].阜阳师范学院学报(自然科学版),1988(2). |
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| 作者姓名： | 袁俊华 |
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| 作者单位： | 蚌埠教育学院 |
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| 摘 要： | 本文利用数学分析,代数的基本理论对线性混合型微分方程的特征根在复平面上的分布作了初步讨论,从而得出:对于n阶混合型线性方程其特征根在一定条件下必分布在某直线的一边,而对于时滞项只含有n次项的n阶线性混合型微分方程,其特征根在一定条件下必分布在以y轴为对称轴的带状区域中,并在此基础上给出了混合型线性微分方程的所有指数解是渐近稳定(或不稳定)的一个充分条件,最后给出了Lecorun方程解稳定的代数判据。
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ABOUT THE DISTRIBUTION OF CHARACTERISTIC ROOT OF LINER MIXE-TYPE DIFFERENTIAL EQUATION OF ORDER N |
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| Abstract: | In this paper, the distribution of chaiacteristic root of liner mixed-type differential epuation on complex plane(s) is discussed in terms of algebra, mathematical analysis basic theorems and the following results are obtained. If time lag term for liner mixe-type differential equation contain only n-th term, its characteristic root must be distributed over range of under certain conditions. And if equation is liner mixe-type differential equation of order n,its characteristc root must be distributed over one side of a straight line under certain conditions. On the basis of above it is obtained that all exponents solution of liner mixed-type epuation is the sufficient condition of asymp—totical stability (or not stability)and the stability algebraical criterion of the solution of Lecorun1] equation is given at last. |
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