tailieunhanh - Báo cáo hóa học: " Research Article Nonlinear Integral Inequalities in Two Independent Variables and Their 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 Integral Inequalities in Two Independent Variables and Their Applications | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 32949 11 pages doi 2007 32949 Research Article Nonlinear Integral Inequalities in Two Independent Variables and Their Applications Kelong Zheng Yu Wu and Shengfu Deng Received 10 June 2007 Accepted 27 July 2007 Recommended by Wing-Sum Cheung This paper generalizes results of Cheung and Ma 2005 to more general inequalities with more than one distinct nonlinear term. From our results some results of Cheung and Ma 2005 can be deduced as some special cases. Our results are also applied to show the boundedness of the solutions of a partial differential equation. Copyright 2007 Kelong Zheng 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 integral inequalities play a fundamental role in the study of existence uniqueness boundedness stability invariant manifolds and other qualitative properties of solutions of the theory of differential and integral equations. There are a lot of papers investigating them such as 1-8 . In particular Pachpatte 2 discovered some new integral inequalities involving functions of two variables. These inequalities are applied to study the boundedness and uniqueness of the solutions of the following terminal value problem for the hyperbolic partial differential equation with conditions D1D2u x y h x y u x y r x y u x 00 ơo x u o y To y u o to k. Cheung 9 and Dragomir and Kim 10 11 established additional Gronwall-Ou-Iang type integral inequalities involving functions of two independent variables. Meng and Li 12 generalized the results of Pachpatte 2 to certain new integrals. Recently Cheung 2 Journal of Inequalities and Applications and Ma 13 discussed the following inequalities no d s t w u s t dtds y fo o u x y a x y c x y d s t w u s t .