| 一类时滞反应扩散方程的周期解和概周期解 |
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| 引用本文： | 王长有,安世全,方长杰.一类时滞反应扩散方程的周期解和概周期解[J].应用数学,2007,20(2):281-285. |
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| 作者姓名： | 王长有 安世全 方长杰 |
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| 作者单位： | 重庆邮电大学应用数学研究所,重庆,400065 |
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| 基金项目： | 四川省学术与技术带头人培养基金;重庆邮电大学校科研和教改项目 |
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| 摘 要： | 通过构造上、下控制函数，结合上、下解方法及相应的单调迭代方法研究了一类时滞反应扩散方程，证明了在反应项非单调时，如果一雏边值问题存在一对周期（或概周期）上、下解，则方程一定存在唯一的周期（或概周期）解．并给出了二维边值问题周期（或概周期）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 概周期解 上、下解 反应扩散方程 |
| 文章编号： | 1001-9847(2007)02-0281-05 |
| 修稿时间： | 2006-08-28 |
Almost Periodic Solutions and Periodic Solutions of Reaction-diffusion Systems with Time Delays |
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| WANG Chang-you,AN Shi-quan,FANG Chang-jie.Almost Periodic Solutions and Periodic Solutions of Reaction-diffusion Systems with Time Delays[J].Mathematica Applicata,2007,20(2):281-285. |
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| Authors: | WANG Chang-you AN Shi-quan FANG Chang-jie |
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| Institution: | Institute of Applied Mathematics, Chongqing University of Post and Telecommunication, Chongqing 400065, China |
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| Abstract: | In this paper, almost periodic solutions and periodic solution of reactiondiffusion 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 periodic or almost periodic upper and lower solutions then the boundary value problem has a unique periodic solution or almost periodic solution. We also discuss the existence and uniqueness of periodic solution and almost periodic solutions for 2-dimensions boundary value systems. And some known results are extended. |
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| Keywords: | Delay Periodic solution Almost periodic solution Upper and lower solution Reaction-diffusion equation |
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