| 时滞反应扩散方程的周期解 |
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| 引用本文： | 王长有,李树勇,杨治国.时滞反应扩散方程的周期解[J].安徽大学学报(自然科学版),2004,28(3):10-14. |
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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： | 四川省教育厅资助项目，四川省应用基础研究计划 |
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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： | 1000-2162(2004)03-0010-05 |
Periodic solutions of reaction-diffusion systems with time delays |
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| WANG Chang-you,LI Shu-yong,YANG Zhi-guo.Periodic solutions of reaction-diffusion systems with time delays[J].Journal of Anhui University(Natural Sciences),2004,28(3):10-14. |
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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 and its 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 then the boundary value problem has a periodic solution. We also discuss the existence and uniqueness of periodic solutions for 2-dimensions boundary value systems. 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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