一类积分不等式组中未知函数的估计  

The estimation of unknown functions in a class of integral inequalities

作　　者：黄星寿 HUANG Xingshou(School of Mathematics and Statistics,Hechi University,Yizhou,Guangxi 546300,China)

机构地区：[1]河池学院数学与统计学院

出　　处：《贵州师范大学学报（自然科学版）》2020年第1期58-62,共5页Journal of Guizhou Normal University：Natural Sciences

基　　金：国家自然科学基金资助项目(11561019,11161018);广西自然科学基金项目(2016GXNSFAA380090,2016GXNSFAA380125)

摘　　要：研究了一类二维积分不等式组,该不等式组积分号外有非常数因子,不能用向量形式的Gronwall-Bellman型积分不等式进行估计。为了简化主要结果的证明,先引进两个引理,给出只含有一个未知函数的积分不等式中未知函数的估计,接着利用两个引理和变量替换技巧和放大技巧给出不等式组中两个未知函数的估计。该结果可用于研究积分、微分动力系统解的性质。A class of 2-dimensional integral inequalities are studied, which include non-constant factors outside the integral terms, and can not be estimated by Gronwall-Bellman type integral inequalities in vector form. In order to simplify the proof of the main results, this paper first introduces two lemmas and gives the estimation of the unknown function in the integral inequality with only one unknown function. Then, the estimations of the two unknown functions in the inequality group are given by using two lemma and variable substitution techniques and amplification techniques. The results can be used to study the properties of the solutions of the integral and differential dynamical systems.

关 键 词：Gronwall-Bellman型积分不等式 二维积分不等式组 时滞积分不等式 显示估计式 

分 类 号：O175.7[理学—数学]