Uniform Persistence and Periodic Coexistence States in Infinite-dimensional Periodic Semiflows with Applications

This paper is devoted to the study of uniform persistence and periodic coexistence states in infinite dimensional periodic eemiflows. Under a general abstract setting, we prove that the uniform persistence of a periodic semiflow is equivalent to that of its associated Poincarb map, and that the uniform persistence implies the existence of a periodic coexistence state, which generalizes and unifies some related earlier results. As an application, we discuss in detail the periodic Kolmogorov predator-prey reaction-diffusion system with spatial heterogeneity and obtain some sufficient conditions for the uniform persistence and global extinction of the system under consideration.