Periodic Solutions of Semilinear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space

JinRong Wang, X. Xiang and W. Wei

Mathematical Problems in Engineering, 2008, vol. 2008, 1-15

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 -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 -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.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:183489

DOI: 10.1155/2008/183489

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