两个新的三变量非线性积分不等式及其应用

TWO NEW NONLINEAR INTEGRAL INEQUALITIES IN THREE VARIABLES AND THEIR APPLICATIONS

在文献[Pachpatte,Demonstratio Math,2009,XLII,341-351]的基础上,建立了两个新的三变量非线性积分不等式.把参考文献中不等式右端被积因子u推广成u的非线性函数.运用变量替换技巧,放大技巧,积分微分技巧,反函数技巧,常量与变量的辩证关系,给出了不等式中未知函数的估计.推广了文献中相应不等式的结果.最后,用所得结果给出了三变量积分方程解的估计.

In this paper,two new nonlinear integral inequalities in three variables are given on the basis of the literature[Pachpatte,Demonstratio Math,2009,XLⅡ,341-351].In the new integral inequalities,the integral factor is replaced by a nonlinear function in integrand.The estimation of unknown function in the new integral inequalities is given by technique of change of variable,amplification method,integration and differentiation,inverse function,and the dialectical relationship between constants and variables.Then,some existing results in the literature become particular cases of our results.Finally,the new inequalities are used to give estimation of solutions of an integral equation in three variables.