Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 183489, 15 pages
Research Article

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

JinRong Wang,1 X. Xiang,2 and W. Wei2

1College of Computer Science and Technology, Guizhou University, Guiyang, Guizhou 550025, China
2College of Science, Guizhou University, Guiyang, Guizhou 550025, China

Received 17 June 2008; Accepted 19 October 2008

Academic Editor: Fernando Lobo Pereira

Copyright © 2008 JinRong Wang et al. 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.


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 T0-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 T0-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.