| 时滞反应扩散方程有界解周期解的存在唯一性 |
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| 引用本文： | 王长有,胡晓红.时滞反应扩散方程有界解周期解的存在唯一性[J].重庆邮电学院学报(自然科学版),2005,17(5):644-646. |
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| 作者姓名： | 王长有 胡晓红 |
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| 作者单位： | 重庆邮电学院,重庆400065 |
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| 基金项目： | 重庆邮电学院青年科技基金资助项目（A2005-14）;四川省学术与技术带头人基金资助项目（1200321） |
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| 摘 要： | 利用上、下解方法及相应的单调迭代方法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单调迭代方法的局限性.为讨论反应项非单调的微分方程提供了一种有效方法,并获得了此方程解的有界性及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 有界解 周期解 上下解 反应扩散方程 |
| 文章编号： | 1004-5694（2005）05-0644-03 |
| 收稿时间： | 2005-01-08 |
| 修稿时间： | 2005-06-22 |
Existence and uniqueness of bounded solution periodic solution of reaction-diffusion equation with time delay |
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| WANG Chang-you, HU Xiao-hong.Existence and uniqueness of bounded solution periodic solution of reaction-diffusion equation with time delay[J].Journal of Chongqing University of Posts and Telecommunications(Natural Sciences Edition),2005,17(5):644-646. |
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| Authors: | WANG Chang-you HU Xiao-hong |
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| Institution: | Chongqing University of Posts and Telecommunications, Chongqing 400065 ,P. R. China |
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| Abstract: | In this paper,bounded solution and periodic solution of reaction-diffusion equation with time delay are investigated.By constructing the upper and lower control function of the reaction function with non-monotone and using the method of upper and lower solutions,the authors demonstrate that the constructed function satisfy the Lipschits condition and monotont,and that it covercome the shortness of the reaction function with non-monotone.It is shown that if the reaction function in the system is non-monotone and the boundary value,then the system has a pair of coupled-upper and lower solutions,and the equation has a unique periodic solution.And some known results are widely used. |
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| Keywords: | time delay bounded solution periodic solution upper and lower solution reaction-diffusion equation |
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