Bounded and Periodic Solutions of Semilinear Impulsive Periodic System on Banach Spaces. (23rd September 2008) - Wang, JinRong; Xiang, X.; Wei, W.; Chen, Qian
Abstract : A class of semilinear impulsive periodic system on Banach spaces is considered. First, we introduce theT 0 -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 ofT 0 -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.