一类时滞抛物型系统周期解的存在稳定性

Existence and stability of periodic solutions for parabolic systems with time delays

利用上、下解方法及不动点理论研究了一类反应项非单调的时滞抛物型系统,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,并获得了此系统边值问题周期解存在性的充分条件;另外,还给出了证明其周期解稳定性的方法,推广了已有的一些结果.

In this paper, periodic solutions of parabolic systems with time delays are investigated. It is constructed that the upper and lower control function of nonmonotone reaction term, and it is showed that the function satisfies a global Lipschitz condition and quasimonotone.A sort of effective method of studying differential equation with nonmonotone reaction term is gained. By using the method of upper and lower solutions and fixed point theorem, it is shown that periodic solutions of this system exist when reaction-term is not monotone and the boundary value system has a pair of coupled -upper and lower solutions. Some methods for proving the stability of the periodic solution are also given. And some known results are extended.