一类非线性Volterra-Fredholm型四重无穷积分不等式  

A Class of Nonlinear Volterra-Fredholm Type Integral Inequality Involving Four Iterated Infinite Integral

作　　者：林远华[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：《四川师范大学学报（自然科学版）》2017年第2期184-188,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11561019和11161018);广西自然科学基金(2016GXNSFAA380090和2012GXNSFAA053009);广西高等学校科研项目(KY2015ZD103和LX2014330)

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.最后,为了说明所得结果的有效性,举例说明所得结果可以用来估计一类四重积分方程解的模.A class of nonlinear Volterra-Fredholm type four iterated integral inequalities with variable lower limit and infinite upper limit is studied.Firstly,the conditions satisfied by known functions in the inequalities are supposed,then estimation for the unknown function in Volterra-Fredholm type integral inequalities is given by analytic techniques,such as change of variable,amplification of inequality,differentiation and integration,inverse function etc.Finally,in order to illustrate the validity of the established results,an application is presented,in which explicit bounds for the solutions of a class of Volterra-Fredholm type four iterated integral equations are deduced.

关 键 词：Volterra-Fredholm型积分不等式 无穷积分 变下限积分 未知函数的估计 

分 类 号：O175.5[理学—数学]