时滞反应扩散方程的周期解

Periodic solutions of reaction-diffusion systems with time delays

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。

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.