| 含时滞的反应扩散方程组周期解的存在与稳定性 |
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| 引用本文： | 王长有,王术,李林锐.含时滞的反应扩散方程组周期解的存在与稳定性[J].数学杂志,2010,30(2). |
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| 作者姓名： | 王长有 王术 李林锐 |
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| 作者单位： | 1. 北京工业大学应用数理学院,北京,100022;重庆邮电大学网络化控制与智能仪器仪表教育部国家重点实验室,重庆,400065;重庆邮电大学数理学院,重庆,400065
2. 北京工业大学应用数理学院,北京,100022 |
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| 基金项目： | 重庆市教育委员会科学技术研究项目，重庆市科委自然科学基金计划项目，北京工业大学博士研究生创新计划项目 |
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| 摘 要： | 本文研究了一类反应项非单调的时滞反应扩散方程组.利用上、下解方法及不动点理论获得了此系统边值问题周期解存在性的充分条件,给出了证明其周期解稳定性的方法.最后通过化学中的一个典型模型说明了所得结果的意义.
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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 存在与稳定性 |
EXISTENCE AND STABILITY OF PERIODIC SOLUTIONS FOR REACTION-DIFFUSION SYSTEMS WITH TIME DELAYS |
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| WANG Chang-you,WANG Shu,LI Lin-rui.EXISTENCE AND STABILITY OF PERIODIC SOLUTIONS FOR REACTION-DIFFUSION SYSTEMS WITH TIME DELAYS[J].Journal of Mathematics,2010,30(2). |
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| Authors: | WANG Chang-you WANG Shu LI Lin-rui |
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| Institution: | WANG Chang-you1,2,3,WANG Shu1,LI Lin-rui1(1.College of Applied Math., Physics,Beijing University of Technology,Beijing 100022,China)(2.Key Laboratory of Network Control , Intelligent Instrument of Ministry of Education,Chongqing University of Posts , Telecommunications,Chongqing 400065,China)(3.College of Math., Physics,China) |
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| Abstract: | In this article,periodic solutions of reaction-diffusion systems with nonmonotone reaction functions and time delays are investigated.By using the method of upper and lower solutions and fixed point theorem,it is shown that periodic solutions of this system exist when the boundary value system has a pair of coupled-upper and lower solutions.Some methods for proving the stability of the periodic solution are also given.Finally,a model arised from chemistry is used to illustrate the obtained results. |
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| Keywords: | delay periodic solution upper and lower solution reaction-diffnsion systems fixed point theorem existence and stability |
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