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 A New Nonlinear Retarded Integral Inequality and Its Application | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 462163 9 pages doi 2010 462163 Research Article A New Nonlinear Retarded Integral Inequality and Its Application Wu-Sheng Wang 1 Ri-Cai Luo 1 and Zizun Li2 1 Department of Mathematics Hechi University Guangxi Yizhou 546300 China 2 School of Mathematics and Computing Science Guilin University of Electronic Technology Guilin 541004 China Correspondence should be addressed to Wu-Sheng Wang wang4896@ Received 28 April 2010 Revised 9 July 2010 Accepted 15 August 2010 Academic Editor Laszlo Losonczi Copyright 2010 Wu-Sheng Wang 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. The main objective of this paper is to establish a new retarded nonlinear integral inequality with two variables which provide explicit bound on unknown function. This inequality given here can be used as tool in the study of integral equations. 1. Introduction Being important tools in the study of differential equations integral equations and integrodifferential equations various generalizations of Gronwall inequality and their applications have attracted great interests of many mathematicians. Some recent works can be found for example in 1-7 and some references therein. Agarwal et al. 1 studied the inequality n bitt u tf a tf j gi t s wi u s ds t0 t t1. Agarwal et al. 2 obtained the explicit bound to the unknown function of the following retarded integral inequality n aRt tp u ty c uq s i s 1 u s gi s 2 log u s ds. 2 Journal of Inequalities and Applications Cheung 3 investigated the inequality in two variables p Ịb1 x r My up x y a g1 s t uq s t dtds 0 p rbi x fC2 y ------J J g2 s t uq s t p u s t dt ds. Chen et al. 4 discussed the following inequality in two variables r x My qf u x y c g s t w u s t dtds Ja x0
