一类变下限非线性Volterra-Fredholm型积分不等式及其应用  

A Class of Nonlinear Volterra-Fredholm Type Integral Inequality with Variable Lower Limit and Its Application

作　　者：侯宗毅[1] 王五生[1] 

机构地区：[1]河池学院数学与统计学院,广西宜州546300

出　　处：《西南师范大学学报（自然科学版）》2016年第2期21-25,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11561019;11161018);广西自然科学基金项目(2012GXNSFAA053009);广西高等学校科研项目(KY2015ZD103)

摘　　要：研究了一类积分上限为无穷大,下限变化的非线性Volterra-Fredholm型迭代四重积分不等式.首先假定不等式中的已知函数应该满足的条件,然后利用分析技巧:比如变量替换、不等式放大、积分微分、反函数等,给出Volterra-Fredholm不等式中未知函数的估计.A class of nonlinear Volterra-Fredholm type integral inequality with variable lower limit and infinite upper bound has beenstudied.Supposing the conditions of known functions in the inequality,the estimation for the unknown function has been given by integral inequality techniques,such as amplification method,differential and integration,change of variable,inverse function,and the dialectical relationship between constants and variables.Finally,to illustrate the validity of the result on the established inequalities,we apply our result to a class of Volterra-Fredholm type integral equations for estimation of unknown function.

关 键 词：积分不等式 不等式技巧 积分方程 解的估计 

分 类 号：O175.5[理学—数学]