| 含时滞的反应扩散方程周期解的存在唯一性 |
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| 引用本文： | 王长有,李树勇,杨治国.含时滞的反应扩散方程周期解的存在唯一性[J].四川师范大学学报(自然科学版),2004,27(4):339-342. |
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| 作者姓名： | 王长有 李树勇 杨治国 |
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| 作者单位： | 四川师范大学,数学与软件科学学院,四川,成都,610066 |
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| 基金项目： | 四川省应用基础研究基金，四川省教育厅重点基金资助项目 |
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| 摘 要： | 通过构造上、下控制函数，结合上、下解及单调迭代方法研究了一类时滞反应扩散方程的周期解，证明了如果反应项非单调且一维边值问题存在一对周期上、下解，则方程一定存在唯一的周期解．并给出了二维边值问题周期解存在唯一性的充分条件，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 |
| 文章编号： | 1001-8395(2004)04-0339-04 |
| 修稿时间： | 2003年10月16 |
Existence and Uniqueness of Periodic Solution of Reaction-diffusion Equation with Time Delay |
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| WANG Chang-you,LI Shu-yong,YANG Zhi-guo.Existence and Uniqueness of Periodic Solution of Reaction-diffusion Equation with Time Delay[J].Journal of Sichuan Normal University(Natural Science),2004,27(4):339-342. |
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| Authors: | WANG Chang-you LI Shu-yong YANG Zhi-guo |
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| Abstract: | In this paper, periodic solutions of reaction-diffusion systems with time delays are investigated. By constructing the upper and lower control function and using the method of upper and lower solutions as well as associated monotone iterations, it is shown that if the reaction function in the system is non-monotone and the 1-dimension boundary value system has a pair of coupled-upper and lower solutions, and then the boundary value problem has a periodic solution. The existence and uniqueness of periodic solutions for 2-dimensions boundary value systems are also discussed. And some known results are extended. |
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| Keywords: | Delay Periodic solution Upper and lower solution Reaction-diffusion system |
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