引用本文:黄星寿, 王五生, 罗日才.一类含有未知导函数的三重积分不等式中未知函数的估计[J].西南师范大学学报(自然科学版),2019,44(7):8~16
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一类含有未知导函数的三重积分不等式中未知函数的估计
黄星寿, 王五生, 罗日才
河池学院 数学与统计学院, 广西 宜州 546300
摘要:
研究了一类非线性三重积分不等式,其中被积函数中含有未知函数及其导函数,积分项外包含了非常数项.利用变量替换技巧、放大技巧和反函数技巧等分析手段,给出了三重积分-微分不等式中未知函数的显上界估计,推广了已有结果.最后举例说明所得结果可以用来研究微分-积分方程解的估计.
关键词:  非线性积分不等式  含有未知导函数的三重积分  微分-积分方程  显式估计
DOI:10.13718/j.cnki.xsxb.2019.07.002
分类号:O175.5
基金项目:国家自然科学基金项目(11561019,11161018);广西自然科学基金项目(2016GXNSFAA380090,2016GXNSFAA380125).
Estimation of Unknown Function of a Class of Triple Integral Inequalities with Unknown Derivative Function
HUANG Xing-Shou, WANG Wu-Sheng, LUO Ri-Cai
School of Mathematics and Statistics, Hechi University, Yizhou Guangxi 546300, China
Abstract:
Gronwall type integral inequality is the important tool in the study of existence, uniqueness, boundedness and other qualitative properties of solutions of differential equations, integral equation and integro-differential equations. In this paper, a class ofnonlineartriple integral inequality is studied, which includes an unknown function and its derivative function in integrand function, and a nonconstant factor outside integral sign. The upper bounds of the unknown function in the integro-differential inequality is estimated explicitly using the techniques of change of variable, the method of amplification, and inverse function technique, which generalized some known results. The derived results can be applied in the study ofthe explicit upper bounds of solutions of a class of integro-differential equations.
Key words:  nonlinear integral inequality  triple integral with unknown derivative function  integro-differential equation  explicit estimation
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