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Báo cáo hóa học: " Research Article Nonlinear Retarded Integral Inequalities with Two Variables and 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 Nonlinear Retarded Integral Inequalities with Two Variables and Applications | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 240790 21 pages doi 10.1155 2010 240790 Research Article Nonlinear Retarded Integral Inequalities with Two Variables and Applications Wu-Sheng Wang 1 2 Zizun Li 1 Yong Li 3 and Yong Huang3 1 School of Mathematics and Computing Science Guilin University of Electronic Technology Guilin 541004 China 2 Department of Mathematics Hechi University Guangxi Yizhou 546300 China 3 Department of Mathematics and Computer Information Engineering Baise College Guangxi Baise 533000 China Correspondence should be addressed to Wu-Sheng Wang wang4896@126.com Received 8 June 2010 Revised 27 August 2010 Accepted 6 October 2010 Academic Editor Sever Silverstru Dragomir 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. We consider some new nonlinear retarded integral inequalities with two variables which extend the results in the work of W.-S. Wang 2007 and the one in the work of Y.-H. kim 2009 . These inequalities include not only a nonconstant term outside the integrals but also more than one distinct nonlinear integrals without assumption of monotonicity. Finally we give some applications to the boundary value problem of a partial differential equation for boundedness and uniqueness. 1. Introduction Integral inequalities that give explicit bounds on unknown functions provide a very useful and important device in the study of many qualitative as well as quantitative properties of solutions of partial differential equations integral equations and integrodifferential equation. One of the best known and widely used inequalities in the study of nonlinear differential equations is Gronwall inequality 1 which states that if u and f are nonnegative continuous functions on the interval a b satisfying u f c