一类非线性Volterra-Fredholm型积分不等式解的估计  

Estimation of unknown function of Volterra-Fredholm type integral inequalities with unknown derivative function in integrand function

作　　者：黄星寿 王五生 HUANG Xingshou;WANG Wusheng(School of Mathematics ＆ Statistics,Ilechi University,Yizhou 54G300,Chin)

机构地区：[1]河池学院数学与统计学院,广西宜州546300

出　　处：《扬州大学学报（自然科学版）》2018年第2期25-27,61,共4页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11561019;11161018);广西省自然科学基金资助项目(2016GXNSFAA380090)

摘　　要：研究一类非线性Volterra-Fredholm型积分不等式,被积函数中含有未知函数及其导函数,积分项外包含非常数项,运用变量替换技巧、放大技巧和反函数技巧等分析手段,给出积分-微分不等式中未知函数的显上界估计,并证明了所得结果可以用来研究微分-积分方程解的估计.In this paper, a class of Volterra Fredholm type integral inequality is studied, which includes an unknown function and its derivative function in integrand function, and a nonconstant term outside integral sign. The upper bounds of the unknown function in the integro differential inequality is estimated explicitly using the techniques of change of variable, the method of amplifica tion, and inverse function technique, which generalize some known results. The derived results can be applied in the study of the explicit upper bounds of solutions of a class of integro differential equations.

关 键 词：VOLTERRA Fredholm型积分不等式 未知函数 导函数 微分积分方程 显示估计 

分 类 号：O175.5[理学—数学]