一类非线性积分不等式组中未知函数的估计  

The Estimation of Unknown Functions in a Class of Nonlinear Integral Inequalities

作　　者：欧阳云 王五生 OUYANG Yun;WANG Wu-sheng(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：《数学的实践与认识》2019年第24期274-280,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11561019,11161018);广西自然科学基金(2016GXNSFAA380090,2016GXNSFAA380125);广西高校中青年教师科研基础能力提升项目(2019KY0625)

摘　　要：研究了一类二维非线性积分不等式组,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.先利用Bernoulli不等式把非线性问题转化成线性问题,利用变量替换技巧和放大技巧研究只含有一个未知函数的积分不等式,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.结果可用于研究积分、微分动力系统解的性质.In this paper,a class of two dimensional nonlinear integral inequalities is studied,which include non-constant factors outside the integral terms,and can not be estimated by Gronwall-Bellman type integral inequalities in vector form.First,the nonlinear problem is transformed into a linear problem by using the Bernoulli inequality.The integral inequality with only one unknown function is studied using variable substitution technique and the magnification technique.The result on the integral inequality of an unknown function is then used to estimate the two unknown functions in a group of inequalities by using two lemma and variable substitution techniques and amplification techniques.The results can be used to study the properties of the solutions of integral and differential dynamical systems.

关 键 词：Gronwall-Bellman型积分不等式 二维积分非线性不等式组 时滞积分不等式 显式估计 

分 类 号：O178[理学—数学] O174[理学—基础数学]