Existence of periodic solutions for hybrid evolution equation with delay in partially ordered Banach spaces

In this paper, we are devoted to consider the periodic problem for the hybrid delayed evolution equation in partially ordered Banach spaces. By means of positive $$C_{0}$$-semigroup and Krasnoselkii type fixed point theorem, we obtain some new existence theorems of periodic mild solutions under some mixed conditions. The results obtained in this paper generalize and improve the recent achievements on this subject. Finally, an example shows the feasibility of the abstract results.