| 时滞反应扩散方程组周期解的存在性 |
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| 引用本文： | 郑继明,王长有.时滞反应扩散方程组周期解的存在性[J].重庆大学学报(自然科学版),2007,30(11):99-102. |
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| 作者姓名： | 郑继明 王长有 |
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| 作者单位： | 重庆邮电大学,应用数学研究所,重庆,400065;重庆邮电大学,应用数学研究所,重庆,400065 |
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| 摘 要： | 利用上、下解方法及不动点理论研究了一类反应项非单调的时滞反应扩散方程组,构造了非单调反应项的上、下控制函数,并证明了所构造的函数满足Lipschitz条件及单调性,克服了反应项非单调无法利用单调迭代方法的局限性,为讨论反应项非单调的微分方程提供了一种有效方法,并获得了此系统边值问题周期解存在性的充分条件,推广了已有的一些结果.
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| 关 键 词： | 时滞 周期解 上、下解 反应扩散方程组 不动点理论 存在性 |
| 文章编号： | 1000-582X（2007）11-0099-04 |
| 修稿时间： | 2007-07-08 |
Existence of Periodic Solutions for Reaction-diffusion Systems with Time Delays |
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| ZHENG Ji-ming,WANG Chang-you.Existence of Periodic Solutions for Reaction-diffusion Systems with Time Delays[J].Journal of Chongqing University(Natural Science Edition),2007,30(11):99-102. |
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| Authors: | ZHENG Ji-ming WANG Chang-you |
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| Institution: | Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065, P R China |
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| Abstract: | Periodic solutions of reaction-diffusion systems with time delays are investigated. The upper and lower control function of nonmonotone reaction term is constructed. It is showed that the function satisfies a global Lipschitz condition and quasimonotone. A sort of effective method of studying differential equation with nonmonotone reaction term is gained. It is shown that periodic solutions of this system exist when reaction-term is not monotone and the boundary value system has a pair of coupled to-upper and lower solutions. |
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| Keywords: | delay periodic solution upper and lower solution reaction-diffusion systems fixed point theorem existence |
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