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

Recommended by Yeol Je Cho

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.