| 一类偏差依赖状态自身的泛函微分方程 |
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| 引用本文： | 吴汉忠.一类偏差依赖状态自身的泛函微分方程[J].数学学报,1995,38(6):803-809. |
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| 作者姓名： | 吴汉忠 |
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| 作者单位： | 宁波师范学院数学系，复旦大学数学研究所 |
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| 摘 要： | 本文证明了一类偏差依赖状态自身的泛函微分方程ｘ′（ｔ）＝ａ（ｔ）ｆ（ｘ（ｔ），ｘ（ｘ（ｔ）））之所有强弱解都必单调，并且首次详尽地研究了方程ｘ′（ｔ）＝ａｘ（ｔ）＋ｂｘ（ｘ（ｔ）），ａ·ｂ≠０强解的存在性及渐近性态。
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| 关 键 词： | 存在性，渐近性态 |
| 收稿时间： | 1991-4-19 |
| 修稿时间： | 1994-7-2 |
A Class of Functional Differential Equations with Deviating Arguments Depending on the State |
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| Wu Hanzhong.A Class of Functional Differential Equations with Deviating Arguments Depending on the State[J].Acta Mathematica Sinica,1995,38(6):803-809. |
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| Authors: | Wu Hanzhong |
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| Institution: | Wu Hanzhong(Department of Mathematics,Ningbo Normal College,Ningbo 3152 1 1,China) |
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| Abstract: | In this paper,it is proved that every strong or weak solution must be monotone fora class of functional differential equations x′(t)=a(t)f(x(t),x(x(t))),the deviating argument ofwhich depends on its state. It is the first time to study in detial for the existences and asymptoticbehaviors of strong solutions for the equation x′(t)=ax(t) + bx(x(t)),a·b≠0. |
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| Keywords: | existence asymptotic behavior |
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