| 引用本文: | 李志祥,唐扬斌.微分方程的有界性与概周期解的存在性.[J].国防科技大学学报,1999,21(3):118-122.[点击复制] |
| Li Zhixiang,Tang Yangbin.On Boundedness of Solutions and Existence of Almost Periodic Solution of Differential Equation[J].Journal of National University of Defense Technology,1999,21(3):118-122[点击复制] |
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| 微分方程的有界性与概周期解的存在性 |
| 李志祥, 唐扬斌 |
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(国防科技大学 系统工程与数学系 湖南 长沙 410073)
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| 摘要: |
| 本文考虑高维非自治概周期系统dx/dt=f(t,x), 利用对x的分量分组构造Liapunov函数的方法讨论了其概周期解的存在性。所得结果去掉了文献中系统存在有界解的假设, 得到了比较明显的改进。 |
| 关键词: Liapunov 函数, 概周期, 一致有界, 一致最终有界 |
| DOI： |
| 投稿日期：1999-01-20 |
| 基金项目: |
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| On Boundedness of Solutions and Existence of Almost Periodic Solution of Differential Equation |
| Li Zhixiang, Tang Yangbin |
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(Department of System Engineering and Applied Mathematics, NUDT, Changsha, 410073)
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| Abstract: |
| In this paper, we consider a higher dimensional nonautonomous almost periodic system dx/dt=f(t,x). By constructing Liapunov functions to groups of quantities of vector x, we diminish the assumption of existence of bounded solution and improve the results in the documents. |
| Keywords: Liapunov function, almost periodic, uniform boundedness, uniformly ultimate boundedness |
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