- Research Article
- Open access
- Published:
The Generalized Gronwall Inequality and Its Application to Periodic Solutions of Integrodifferential Impulsive Periodic System on Banach Space
Journal of Inequalities and Applications volume 2008, Article number: 430521 (2008)
Abstract
This paper deals with a class of integrodifferential impulsive periodic systems on Banach space. 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's inequality with impulse, mixed type integral operators and -norm given by us, we utilize Leray-Schauder fixed point theorem to prove the existence of -periodic PC-mild solutions. Our method is much different from methods of other papers. At last, an example is given for demonstration.
Publisher note
To access the full article, please see PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Wang, J.R., Xiang, X., Wei, W. et al. The Generalized Gronwall Inequality and Its Application to Periodic Solutions of Integrodifferential Impulsive Periodic System on Banach Space. J Inequal Appl 2008, 430521 (2008). https://doi.org/10.1155/2008/430521
Received:
Accepted:
Published:
DOI: https://doi.org/10.1155/2008/430521