Skip to main content


  • Research Article
  • Open Access

Bounded and Periodic Solutions of Semilinear Impulsive Periodic System on Banach Spaces

Fixed Point Theory and Applications20082008:401947

  • Received: 20 February 2008
  • Accepted: 7 July 2008
  • Published:


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.


  • Banach Space
  • Periodic Solution
  • Differential Geometry
  • Evolution Operator
  • Computational Biology

Publisher note

To access the full article, please see PDF.

Authors’ Affiliations

College of Computer Science and Technology, Guizhou University, Guiyang, Guizhou, 550025, China
College of Science, Guizhou University, Guiyang, Guizhou, 550025, China
College of Electronic Science and Information Technology, Guizhou University, Guiyang, Guizhou, 550025, China


© JinRong Wang et al. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.