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 on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 283926 11 pages doi 2011 283926 Research Article Nonlinear Integral Inequalities in Two Independent Variables on Time Scales Wei Nian Li Department of Mathematics Binzhou University Shandong 256603 China Correspondence should be addressed to Wei Nian Li wnli@ Received 7 December 2010 Accepted 18 February 2011 Academic Editor Jianshe Yu Copyright 2011 Wei Nian Li. 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 investigate some nonlinear integral inequalities in two independent variables on time scales. Our results unify and extend some integral inequalities and their corresponding discrete analogues which established by Pachpatte. The inequalities given here can be used as handy tools to study the properties of certain partial dynamic equations on time scales. 1. Introduction The theory of dynamic equations on time scales unifies existing results in differential and finite difference equations and provides powerful new tools for exploring connections between the traditionally separated fields. During the last few years more and more scholars have studied this theory. For example we refer the reader to 1 2 and the references cited therein. At the same time some integral inequalities used in dynamic equations on time scales have been extended by many authors 3-11 . On the other hand a few authors have focused on the theory of partial dynamic equations on time scales 12-17 . However only 10 11 have studied integral inequalities useful in the theory of partial dynamic equations on time scales as far as we know. In this paper we investigate some nonlinear integral inequalities in two independent variables on time scales which can be used as handy tools to study the properties of certain partial dynamic .
