一类时滞反应扩散方程的周期解和概周期解

In this paper, almost periodic solutions and periodic solution 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 periodic or almost periodic upper and lower solutions then the boundary value problem has 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.