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 Correspondence should be addressed to Wing-Sum Cheung, [email protected] Received 9 May 2008; Revised 26 November 2008; Accepted 29 January 2009 Recommended by Alexander Domoshnitsky 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. Copyright q 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.