一类积分号外具有非常数因子的弱奇异时滞积分不等式

A Class of Weakly Singular Retarded Integral Inequality with a Nonconstant Factor Outside Integral Sign

研究了一类积分号外具有非常数因子的非线性弱奇异时滞积分不等式.利用离散Jensen不等式、时滞H?lder积分不等式、特殊函数、变量替换和放大技巧等分析手段,给出了不等式中未知函数的上界估计,推广了已有结果.最后应用所得结果研究了弱奇异积分方程解的定性性质.

In this paper,we establish a class of nonlinear retarded weakly singular integral inequalities,which includes a nonconstant factor outside integral sign and a nonconstant term outside integral term.The upper bounds of the embedded unknown functions are estimated explicitly using discrete Jensen inequality,retarded H？lder＇s integral inequality,special function,the techniques of change of variable and the method of amplification.This generalize some known results.The derived results can be applied to the study of qualitative properties of solutions of fractional integral equations.