| 闭区域上微分包含的弱Filippov定理 |
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| 引用本文： | 许宏文,薛小平. 闭区域上微分包含的弱Filippov定理[J]. 黑龙江大学自然科学学报, 2009, 26(2) |
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| 作者姓名： | 许宏文 薛小平 |
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| 作者单位： | 哈尔滨工业大学,数学系,哈尔滨,150001;哈尔滨工业大学,数学系,哈尔滨,150001 |
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| 摘 要： | 考虑变元x约束在闭区域 -Ω上的微分包含的初值问题.对给定的有约束微分包含x'∈F(t,x)的初值问题x(to)=xo 的一个定义在[to,+∞)的AC解及任意的点yo ∈-Ω,证明了存在一个该约束微分包含的满足初始条件yo的定义在[to,+∞)的PC解y(·)且满足|x(t)-y(t)|≤Ceξ(t-to)|xo-yo|,这里F满足单边Lipschitz条件,Ω满足一致内球条件.
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| 关 键 词： | Filippov定理 单边Lipschitz条件 PC解 一致内球条件 |
Weak Filippov's theorem of differential inclusions on closed domains |
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| XU Hong-wen,XUE Xiao-ping. Weak Filippov's theorem of differential inclusions on closed domains[J]. Journal of Natural Science of Heilongjiang University, 2009, 26(2) |
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| Authors: | XU Hong-wen XUE Xiao-ping |
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| Affiliation: | Department of Mathematics;Harbin Institute of Technology;Harbin 150001;China |
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| Abstract: | The initial value problem of the differential inclusion x'∈F(t,x) is investigated,wherethe variable x is constrained to a closed domain -Ω.It is shown that given yo ∈-Ω and an AC solution x |x(t)-y(t)|≤Ceζ(t-to)|xo-yo|,when F is one-side Lipschitz continuous.Ω satisfies the Uniform Internal Sphere Condition. |
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| Keywords: | Filippov'S theorem one-side Lipschitz condition PC solution uniform internal sphere condition |
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