脉冲时滞微分方程的周期性和稳定性研究

Periodicity and Stability in Impulsive Equations with Delays

利用Gaines和Mawhin的重合度理论,给出了一个周期环境下具有分布时滞的脉冲微分方程的正周期解的存在性的判定。与此同时,通过引入分片连续Lyapunov函数的方法,建立了脉冲效应下时滞微分方程的零解稳定性的充分条件。

With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solution of an impulsive equation with a distributed delay in a periodic environment. At the same time, effective sufficient conditions are found for stability via the approach of piece-wise continuous Lyapunov function introduced.