Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 524945, 16 pages
Existence and Global Asymptotical Stability of Periodic Solution for the -Periodic logistic
System with Time-Varying Generating Operators
and -Periodic Impulsive Perturbations on Banach Spaces
1Department of Computer, College of Computer Science and Technology, Guizhou University, Guiyang, Guizhou 550025, China
2Department of Mathematics, College of Science, Guizhou University, Guiyang, Guizhou 550025, China
3Department of Electronic Science, College of Electronic Science and Information Technology, Guizhou University, Guiyang, 550025, China
Received 9 March 2008; Accepted 16 June 2008
Academic Editor: Guang Zhang
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.
This paper studies the existence and global asymptotical stability of periodic PC-mild solution for
the -periodic Logistic system with time-varying generating operators and -periodic impulsive perturbations on
Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator
corresponding to homogenous well-posed -periodic system with time-varying generating operators and -periodic
impulsive perturbations are given. It is shown that the system have a unique periodic PC-mild solution which is globally asymptotically stable when and are rational dependent and its period must be for some . At last, an example is given for demonstration.