一类带有脉冲的中立时滞型微分方程的周期解（英文）

Periodic solutions of a neutral impulsive differential equation

主要考虑了一类带有脉冲的中立时滞型微分方程.研究了一类带有非单调函数响应的脉冲捕食模型,得出该模型不存在周期解和存在至少一个或者两个全局周期解的充分条件.该方法是基于Mawhin重合度和对未知解采用新颖的先验估计技术.实例表明此方法是可行的也是有效的.

In this paper, we consider a neutral impulsive differential equation. An impulsive predator- prey model with non-monotonic functional response is investigated. Some novel sufficient conditions are obtained for the nonexistence of periodic solutions and the global existence of at least one or two positive periodic solutions. Our method is based on Mawhinxs coincidence degree and novel estimation techniques for the priori bounds of unknown solutions. An application is presented to illustrate the feasibility and effectiveness of our main results.