摘要
研究一类非线性积分不等式,被积函数中含有未知函数及其导函数,积分项外包含了非常数项.利用变量替换技巧和放大技巧等分析手段,给出积分-微分不等式中未知函数的上界估计,推广已有结果.最后举例说明所得结果可以用来研究微分-积分方程解的定性性质.
A class of nonlinear integral inequalities is established,which includes a nonconstant factor outside integral sign,an unknown function and its derivative function in integrand function.The upper bound of the unknown function in the integro-differential inequality is estimated explicitly using the techniques of variable substitution and amplification,which generalizes some known results.The derived results can be applied in the study of the explicit upper bounds of solutions of a class for integro-differential equations.
作者
范乐乐
王五生
钟华
FAN Lele;WANG Wusheng;ZHONG Hua(School of Mathematics and Statistics,Hechi University,Yizhou 546300,Guangxi)
出处
《四川师范大学学报（自然科学版）》
CAS
北大核心
2019年第6期816-819,共4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2016GXNSFAA380125)
关键词
非线性积分不等式
含有未知导函数的积分
微分-积分方程
显式估计
nonlinear integral inequality
integral with unknown derivative function
integro-differential equation
explicit estimation
