Periodic solutions of a neutral impulsive differential equation

In this paper, we consider a neutral impulsive differential equation. An impulsive predatorprey 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 Mawhin's 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