一类非连续函数积分不等式及其应用  

A Class of Integral Inequalities for Discontinuous Function and Its Application

作　　者：王五生[1] 李自尊[2] 

机构地区：[1]河池学院数学系,广西宜州546300 [2]百色学院数学与计算机信息工程系,广西百色533000

出　　处：《西南大学学报（自然科学版）》2012年第2期96-100,共5页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11161018);广西自然科学基金资助项目(0991265);河池学院应用数学重点学科(200725);河池学院重点课题(2009YAZ-N001);重点课程<数学建模>(20089)

摘　　要：众所周知,连续函数的Gronwall-Bellman型积分不等式是研究微分方程和积分方程的解的定性性质的重要工具.同样地,非连续函数的积分不等式是研究脉冲微分方程的有用工具.文章研究了具有两个非常数因子的非连续函数的积分不等式,用分析的技巧给出了未知函数的上界估计,并用得到的结果给出了脉冲积分方程解的估计.It is well known that Gronwall-Bellman type integral inequalities are important tools for studying qualitative properties of solutions of differential equations and integral equations,and integral inequalities for dis continuous functions are important tools for impulsive differential equations as well.In the paper,a class of new retarded integral inequalities for discontinuous functions which contain two non-constant factors is studied,and upper bound estimation of the unknown function is discussed by analysis skills.Applying the results,the estimation of solution of impulsive integral equations is obtained.

关 键 词：非连续函数 积分不等式 上界估计 脉冲积分方程 

分 类 号：O178[理学—数学]