一类非线性弱奇异多重积分不等式中未知函数的估计及其应用  

Estimation of unknown function of a class of nonlinear weakly singular triple integral inequality and its application

作　　者：黄基廷[1] 王五生[1] HUANG Ji-ting WANG Wu-sheng(School of Mathematics and Statistics, Hechi University, Yizhou 546300, Guangxi, Chin)

机构地区：[1]河池学院数学与统计学院,广西宜州546300

出　　处：《西北师范大学学报（自然科学版）》2017年第2期8-12,共5页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11561019;11161018);广西自然科学基金资助项目(2012GXNSFA A053009);广西高等学校科研自治项目(KY2015ZD103;KY2015YB257)

摘　　要：研究了一类非线性弱奇异多重积分不等式,被积函数中含有积分变量,积分项外包含了非常数项,利用离散Jensen不等式、Cauchy-Schwarz积分不等式、变量替换技巧和放大技巧等分析手段,给出了不等式中未知函数的上界估计.最后举例说明所得结果可以用来研究弱奇异积分方程解的定性性质.A class of nonlinear weakly singular multiple integral inequalities are investigated in this paper, which include a nonconstant term outside the integrals, and integral variable is included in the integrands in the integral inequality. The upper bounds of the embedded unknown functions are estimated explicitly by adopting some analysis techniques, such as discrete Jensen inequality, Cauchy-Schwarz integral inequality, the techniques of change of variable, and the method of amplification. The derived results can be applied in the study of qualitative properties of solutions of multiple fractional integral equations.

关 键 词：弱奇异三重积分不等式 离散Jensen不等式 Cauchy-Schwarz积分不等式 上界估计 

分 类 号：O175.5[理学—数学]