| 非Lipschitz系数下随机泛函微分方程适度解的存在唯一性及其渐近性态(英文) |
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| 引用本文： | 尹湘锋,刘再明,陈勇,匡能晖.非Lipschitz系数下随机泛函微分方程适度解的存在唯一性及其渐近性态(英文)[J].数学进展,2012(4):473-486. |
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| 作者姓名： | 尹湘锋 刘再明 陈勇 匡能晖 |
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| 作者单位： | 湖南科技大学数学与计算科学学院;中南大学数学与计算技术学院 |
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| 基金项目： | supported by NSFC(No.10971230,No.11101137 and No.11126188);the Natural Science Foundation of Hunan Province(No.10JJ6014);the Research Foundation of Education Bureau of Hunan Province(No.11C0543) |
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| 摘 要： | 本文主要运用Picard迭代和算子分数次幂方法,讨论了随机时滞偏微分方程适度解的存在性与唯一性,并对解的渐近性态进行了研究.这里方程的系数不满足Lipschitz条件,时滞r>0为有限的.最后给出了一个非Lipschitz条件的例子.
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| 关 键 词： | 随机泛函微分方程 时滞 Picard迭代 闭算子分数次幂 |
Existence,Uniqueness and Asymptotic Behavior of Mild Solutions to Stochastic Functional Differential Equations With Non-Lipschitz Coefficients |
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| YIN Xiangfeng,LIU Zaiming,CHEN Yong,KUANG Nenghui.Existence,Uniqueness and Asymptotic Behavior of Mild Solutions to Stochastic Functional Differential Equations With Non-Lipschitz Coefficients[J].Advances in Mathematics,2012(4):473-486. |
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| Authors: | YIN Xiangfeng LIU Zaiming CHEN Yong KUANG Nenghui |
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| Institution: | 1 (1.School of Mathematics and Computing Science,Hunan University of Sciences and technology, Xiangtan,Hunan,411201,P.R.China;2.School of Mathematical Science and Computing Technology, Central South University,Changsha,Hunan,410075,P.R.China) |
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| Abstract: | In the present paper,sufficient conditions are given under which the existence and uniqueness of mild solutions to stochastic partial functional differential equations with finite delay r>0 are obtained using a Picard type method of approximation and the semigroup method,where coefficients of the differential equations are non-Lipschitz.Moreover,the almost sure exponential stability of the mild solution is also studied.An example is given to illustrate our results. |
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| Keywords: | stochastic partial functional differential equation delay Picard approximation fractional power of closed operator |
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