Abstract
A class of semilinear impulsive periodic systems with time‐varying generating operators on Banach space is considered. Using impulsive periodic evolution operator given by us, the T0‐periodic PC‐mild solution is introduced and suitable Poincaré operator is constructed. Showing the compactness of Poincaré operator and using a new generalized Gronwall inequality with mixed type integral operators given by us, we utilize Leray‐Schauder fixed point theorem to prove the existence of T0‐periodic PC‐mild solutions. Our method is an innovation and it is much different from methods of other papers. At last, an example is given for demonstration.
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