| 时滞反应扩散方程周期解的存在性 |
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| 引用本文： | 王长有,李树勇,杨治国.时滞反应扩散方程周期解的存在性[J].四川师范大学学报(自然科学版),2005,28(5):542-545. |
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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： | 1. 重庆邮电学院,计算机科学与技术学院,重庆,400065
2. 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： | 四川省教育厅学术与技术带头人基金资助项目 |
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| 摘 要： | 利用周期上、下解方法及Schauder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,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上、下解方法的局限性,为讨论反应项非单调的微分方程提供了一种有效的方法,并获得了此系统边值问题周期解存在性的充分条件.
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| 关 键 词： | 时滞 周期解 上下解 反应扩散方程 不动点理论 |
| 文章编号： | 1001-8395（2005）05-0542-04 |
| 收稿时间： | 2004-07-04 |
| 修稿时间： | 2004年7月4日 |
Existence of Periodic Solutions of Reaction-diffusion Systems with Time Delays |
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| WANG Chang-you,Li Shu-yong,YANG Zhi-guo.Existence of Periodic Solutions of Reaction-diffusion Systems with Time Delays[J].Journal of Sichuan Normal University(Natural Science),2005,28(5):542-545. |
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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. It is constructed that the upper and lower control function of nonmonotone reaction term, and 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. By using the method of upper and lower solutions and fixed point theorem, it is proved that periodic solutions of this system exist when reaction-term is not monotone and the boundary value system has a pair of coupled-upper and lower solutions. And some known results are extended. |
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| Keywords: | Delay Periodic solution Upper and lower solution Reaction-diffusion system Fixed point theorem |
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