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

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  • JinRong Wang
  • X. Xiang
  • W. Wei

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.

Suggested Citation

  • JinRong Wang & X. Xiang & W. Wei, 2008. "Periodic Solutions of Semilinear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space," Mathematical Problems in Engineering, Hindawi, vol. 2008, pages 1-15, December.
    • Handle: RePEc:hin:jnlmpe:183489
    DOI: 10.1155/2008/183489
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