On some new integral inequalities and their applications q Fan Wei Meng a , Wei Nian Li b, * a Department of Mathematics, Qufu Normal University, Shandong 273165, China b Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, China Abstract The aim of the present paper is to establish some new integral inequalities in two independent variables which provide explicit bounds on unknown functions. The in- equalities given here can be used as tools in the qualitative theory of certain partial differential equations. Ó 2002 Elsevier Inc. All rights reserved. Keywords: Integral inequality; Two independent variables; Partial differential equation 1. Introduction The integral inequalities involving functions of one and more than one in- dependent variables which provide explicit bounds on unknown functions play a fundamental role in the development of the theory of differential equations. During the past few years, many such new inequalities have been discovered, which are motivated by certain applications. For example, see [1–8] and the references therein. In the qualitative analysis of some classes of partial differ- ential equations, the bounds provided by the earlier inequalities are inadequate and it is necessary to seek some new inequalities in order to achieve a diversity of desired goals. In this paper, we establish some new integral inequalities q Supported by the natural science foundation of Shandong province, China (Y2001A03). * Corresponding author. E-mail addresses: fwmeng@qfnu.edu.cn (F.W. Meng), wnli@263.net (W.N. Li). 0096-3003/$ - see front matter Ó 2002 Elsevier Inc. All rights reserved. doi:10.1016/S0096-3003(02)00855-X Applied Mathematics and Computation 148 (2004) 381–392 www.elsevier.com/locate/amc