| 微分方程的有界性与概周期解的存在性 |
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| 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. |
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| 作者姓名： | 李志祥 唐扬斌 |
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| 作者单位： | 国防科技大学系统工程与数学系 |
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| 摘 要： | 本文考虑高维非自治概周期系统ｄｘｄｔ＝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。
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| 关 键 词： | Liapunov函数，概周期，一致有界，一致最终有界 |
| 收稿时间： | 1999/1/20 0:00:00 |
On Boundedness of Solutions and Existence of Almost Periodic Solution of Differential Equation |
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| Li Zhixiang and 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. |
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| Authors: | Li Zhixiang and Tang Yangbin |
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| Institution: | Department of System Engineering and Applied Mathematics, NUDT, Changsha, 410073;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 d x d t=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. |
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| Keywords: | Liapunov function almost periodic uniform boundedness uniformly ultimate boundedness |
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