Abstract
This paper deals with a class of integrodifferential impulsive periodic systems on Banach space. Using impulsive periodic evolution operator given by us, theT0-periodicPC-mild solution is introduced and suitablePoincaréoperator is constructed. By virtue of the generalized new Gronwall lemma with impulse andB-norm, the estimate on thePC-mild solutions is derived. Showing the continuity and compactness of thePoincaréoperator, we utilize Horn's fixed point theorem to prove the existence ofT0-periodicPC-mild solutions when thePC-mild solutions are bounded and ultimate bounded. This extends the study of periodic solutions of integrodifferential periodic system without impulse to integrodifferential periodic system with impulse on general Banach spaces. At last, an example is given for demonstration.
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