| x'=g(x,t)+h(t)型方程的拓扑动力系统与Kurzweil-Henstock积分 |
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| 引用本文： | 李宝麟,薛小平. x'=g(x,t)+h(t)型方程的拓扑动力系统与Kurzweil-Henstock积分[J]. 数学学报, 2003, 46(4): 795-804. DOI: cnki:ISSN:0583-1431.0.2003-04-022 |
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| 作者姓名： | 李宝麟 薛小平 |
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| 作者单位： | [1]西北师范大学数学系兰州730070 [2]哈尔滨工业大学数学系哈尔滨150001 |
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| 基金项目： | 国家自然科学基金资助项目(19671021);NWNU-KJCXGC-212资助项目 |
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| 摘 要： | 本文借助Sell等人建立的局部动力系统理论,利用Kurzweil-Henstock积分,建立了x′=g(x,t)+h(t)型非自治微分方程的拓扑动力系统,为进一步讨论这种方程解的渐近行为作了基础性的工作.本文的工作也是Sell等人工作中有关结论的推广.
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| 关 键 词： | Kurzweil-Henstock积分 局部动力系统 非自治微分方程 |
| 文章编号： | 0583-1431(2003)04-0795-10 |
| 修稿时间： | 2000-12-11 |
Topological Dynamics of Equation of the form x'' = g(x, t) + h(t) and Kurzweil-Henstock Integral |
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| Affiliation: | Bao Lin LI (Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China) Xiao Ping XUE (Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China) |
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| Abstract: | By the theory of local dynamics system defined by Sell, by using the Kurzweil-Henstock integral, the local dynamics system of nonautonomous differential equations form x' = g(x, t) + h(t) is established. These results are of foundational significance of the works for further studying the asymptotic behavior of solutions of equations of the form x' = g(x,t) + hit). These results are also generalizations of some results in the works of Sell (see [1-12]). |
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| Keywords: | Kurzweil-Henstock integral Local dynamics system Nonautonomous differential equation |
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