一类含时滞的抛物型方程组周期解的存在唯一性

Existence and Uniqueness of Periodic Solutions of ParabolicSystems with Time Delays

利用上、下解方法及相应的单调迭代方法研究了一类带离散时滞的抛物型方程组的周期解,证明了如果反应项混拟单调且边值问题存在一对周期上、下解,则方程一定存在一对周期拟解,并且拟解构成的区间是一个吸引子,在某些条件下,周期拟解恰好就是方程的周期解.最后以一个生态模型为例说明了所得结果的意义.

In this paper, periodic solutions of semilinear parabolic equations with discrete time delays are inrestigated. By using the method of upper and lower solutions and its associated monotone iterations, it is shown that if the reaction function in the system possesses a mixed quasimonotone property and the periodic boundary ralue system has a pair of coupled T-upper and lower solutions then the periodic boundary ralue problem has a pair of periodic quasisolutions and the sector between the quasisolutions is an attractor of the delayed periodic parabolic system. Under some additional conditions the periodic quasisolution are exactly true periodic solutions the periodic boundary value system. Finally, a model arising from ecology is given to illustrate the obtained results.