带参数的Gronwall不等式在微分方程中的应用  

Application of Gronwall Inequality with Parameters in Differential Equations

作　　者：王彦朝[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《绵阳师范学院学报》2016年第2期8-10,共3页Journal of Mianyang Teachers＇ College

摘　　要：Gronwall不等式在微分方程中的巨大作用,让其在不等式和微分方程的研究中都处于重要的地位.现在我们利用一种辅助函数,将Gronwall不等式与一阶常微分方程联系起来,用我们常用的求解常微分方程的积分因子法得到了一个带参数α的Gronwall不等式的推广形式.另外,我们可以用同样的方法给出了Gronwall不等式的一个证明.The use of Gronwall inequality is so important that it is a focus which is always researched. In this paper,Gronwall inequality is related to first order Ordinary Differential equations. Using the method of auxiliary function,a generalized form on Gronwall inequality with a parameter α is obtained by the integral factor method which is used to solve ordinary differential equation with order one. In addition,another proof of Gronwall inequality is listed.

关 键 词：辅助函数 积分因子法 一阶常微分方程 Yong不等式 

分 类 号：O178[理学—数学]