Abstract
In this paper, a class of semilinear impulsive periodic systems on Banach space is considered. Using impulsive periodic evolution operator, the T 0 -periodic P C -mild solution is introduced and suitable Poincaré operator is constructed. Showing the compactness of the Poincaré operator and using a new generalized Gronwall inequality with mixed type integral operators, we utilize the Leray–Schauder fixed point theorem to prove the existence of the T 0 -periodic P C -mild solutions. Our method is much different from methods of other papers. An example illustrates the applicability of our results.
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