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| 具两个时滞项的微分方程的稳定性 | |
| 引用本文： | 曾志刚,廖晓昕. 具两个时滞项的微分方程的稳定性[J]. 应用数学学报, 2004, 27(3): 489-499 |
| 作者姓名： | 曾志刚 廖晓昕 |
| 作者单位： | 1. 湖北师范学院数学系,黄石,435002;中国科学技术大学自动化系,合肥,230026 2. 华中科技大学控制科学与工程系,武汉,430074 |
| 基金项目： | 国家自然科学基金(60274007号)，湖北省教育厅优秀青年项目(20038001号)，“面向21世纪教育振兴行动计划”资助项目. |
| 摘 要： | 本文考虑了一类具两个时滞项的微分方程的稳定性，其中一个时滞项的系数非负，另一个时滞项的系数非正．当非负系数恒为零时，本文所得结论改进了Yorke等提出的3/2稳定性定理的相应结论，当非负系数项的时滞为零，本文不同于已有文献用Liapunov函数或泛函法将时滞项作为干扰处理，而是反过来利用时滞项让方程稳定． |
| 关 键 词： | 时滞微分方程 Liapunov函数 Yorke条件 稳定性 单调 |
STABILITY OF DIFFERENTIAL EQUATIONS WITH TWO DELAYS |
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| ZENG ZHIGANG,LIAO XIAOXIN. STABILITY OF DIFFERENTIAL EQUATIONS WITH TWO DELAYS[J]. Acta Mathematicae Applicatae Sinica, 2004, 27(3): 489-499 | |
| Authors: | ZENG ZHIGANG LIAO XIAOXIN |
| Abstract: | The stability of differential equations with two delays is considered in this paper. The coefficient of one delay term is nonnegative, that of the other is nonpositive. When nonnegative coefficient identically vanishing, the 3/2 stability theorem, which Yorke and the other researchers presented, was improved and generalized. When delay of nonnegative coefficient term identically vanishing, our results have shown that the delay term can make the unstable equations stable. This is different from the Lyapunov function or Lyapunov functional way which regard the delay term as disturber. |
| Keywords: | Equation with delay the 3/2 stability Yorke condition monotone |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |