Open Access

New Retarded Integral Inequalities with Applications

Journal of Inequalities and Applications20082008:908784

DOI: 10.1155/2008/908784

Received: 29 January 2008

Accepted: 24 April 2008

Published: 29 April 2008

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.

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Authors’ Affiliations

(1)
Department of Mathematical Sciences, Florida Institute of Technology
(2)
Department of Applied Mathematics, College of Natural Sciences Changwon National University Changwon

Copyright

© Ravi P. Agarwal et al. 2008

This article is published under license to BioMed Central Ltd. 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.