Bounded and Periodic Solutions of Semilinear Impulsive Periodic System on Banach Spaces
© JinRong Wang et al. 2008
Received: 20 February 2008
Accepted: 7 July 2008
Published: 14 July 2008
A class of semilinear impulsive periodic system on Banach spaces is considered. First, we introduce the -periodic PC-mild solution of semilinear impulsive periodic system. By virtue of Gronwall lemma with impulse, the estimate on the PC-mild solutions is derived. The continuity and compactness of the new constructed Poincaré operator determined by impulsive evolution operator corresponding to homogenous linear impulsive periodic system are shown. This allows us to apply Horn's fixed-point theorem to prove the existence of -periodic PC-mild solutions when PC-mild solutions are ultimate bounded. This extends the study on periodic solutions of periodic system without impulse to periodic system with impulse on general Banach spaces. At last, an example is given for demonstration.
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