Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 258569, 15 pages
doi:10.1155/2009/258569
Research Article

Gronwall-Bellman-Type Integral Inequalities and Applications to BVPs

Chur-Jen Chen, Wing-Sum Cheung, and Dandan Zhao

Department of Mathematics, Tunghai University, Taichung, Taiwan

Received 9 May 2008; Revised 26 November 2008; Accepted 29 January 2009

Academic Editor: Alexander Domoshnitsky

Copyright © 2009 Chur-Jen Chen 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.

Abstract

We establish some new nonlinear Gronwall-Bellman-Ou-Iang type integral inequalities with two variables. These inequalities generalize former results and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of differential equations. Example of applying these inequalities to derive the properties of BVPs is also given.