tailieunhanh - Báo cáo hóa học: "Research Article New Retarded Integral Inequalities with Applications"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article New Retarded Integral Inequalities with Applications | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 908784 15 pages doi 2008 908784 Research Article New Retarded Integral Inequalities with Applications Ravi P. Agarwal 1 Young-Ho Kim 2 and S. K. Sen1 1 Department of Mathematical Sciences Florida Institute of Technology 150 West University Boulevard Melbourne FL 32901 USA 2 Department of Applied Mathematics College of Natural Sciences Changwon National University Changwon Kyeongnam 641-773 South Korea Correspondence should be addressed to Young-Ho Kim yhkim@ Received 29 January 2008 Accepted 24 April 2008 Recommended by Yeol Je Cho 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. 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. 1. Introduction The celebrated Gronwall inequality 1 states that if u and f are nonnegative continuous functions on the interval a b satisfying uịt c i f s u s ds t G a b a for some constant c 0 then u t c exp f s ds t G a b . a Since the inequality provides an explicit bound to the unknown function u and hence furnishes a handy tool in the study of solutions of differential equations. Because of its 2 Journal of Inequalities and Applications fundamental importance several generalizations and analogous results of the inequality have been established over years. Such generalizations are in general .