TAILIEUCHUNG - Báo cáo sinh học: " Research Article Some Nonlinear Integral Inequalities in Two Independent Variables"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Some Nonlinear Integral Inequalities in Two Independent Variables | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 984141 14 pages doi 2010 984141 Research Article Some Nonlinear Integral Inequalities in Two Independent Variables Wei Nian Li1 2 1 Department of Mathematics Binzhou University Shandong 256603 China 2 School of Mathematics Science Qufu Normal University Shandong 273165 China Correspondence should be addressed to Wei Nian Li wnli@ Received 14 January 2010 Accepted 29 May 2010 Academic Editor Binggen Zhang Copyright 2010 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 new nonlinear integral inequalities in two independent variables. The inequalities given here can be used as tools in the qualitative theory of certain nonlinear partial differential equations. 1. Introduction It is well known that the integral inequalities involving functions of one and more than one independent variables which provide explicit bounds on unknown functions play a fundamental role in the development of the theory of differential equations. In the past few years a number of integral inequalities had been established by many scholars which are motivated by certain applications. For details we refer to literatures 1-10 and the references therein. In this paper we investigate some new nonlinear integral inequalities in two independent variables which can be used as tools in the qualitative theory of certain partial differential equations. 2. Main Results In what follows R denotes the set of real numbers and R 0 to is the given subset of R. The first-order partial derivatives of a z x y defined for x y e R with respect to x and y are denoted by zx x y and zy x y respectively. Throughout this paper all the functions which appear in the inequalities are assumed to be real-valued and all the integrals .

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