Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 908784, 15 pages
doi:10.1155/2008/908784
Research Article

New Retarded Integral Inequalities with Applications

Ravi P. Agarwal,1 Young-Ho Kim,2 and S. K. Sen1

1Department of Mathematical Sciences, Florida Institute of Technology, 150 West University Boulevard, Melbourne, FL 32901, USA
2Department of Applied Mathematics, College of Natural Sciences Changwon National University Changwon, Kyeongnam 641-773, South Korea

Received 29 January 2008; Accepted 24 April 2008

Academic Editor: Yeol Je Cho

Copyright © 2008 Ravi P. Agarwal 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

Some new nonlinear integral inequalities of Gronwall type for retarded functions are established, which extend the results Lipovan (2003) and Pachpatte (2004). These inequalities can be used as basic tools in the study of certain classes of functional differential equations as well as integral equations. A existence and a uniqueness on the solution of the functional differential equation involving several retarded arguments with the initial condition are also indicated.