UNIFORM PERSISTENCE AND PERIODIC
COEXISTENCE STATES IN INFINITE-DIMENSIONAL
PERIODIC SEMIFLOWS WITH APPLICATIONS

XIAO-QIANG ZHAO

Abstract. This paper is devoted to the study of uniform persistence and periodic coexistence states in infinite dimensional periodic semiflows. Under a general abstract setting, we prove that the uniform persistence of a periodic semiflow is equivalent to that of its associated Poincaré 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.