弱奇异非线性迭代积分不等式及其应用  

Weakly Singular Nonlinear Iterated Integral Inequality with Its Applications

作　　者：黄春妙[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）》2016年第2期214-220,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11561019;11161018);广西自然科学基金(2012GXNSFAA053009);广西高等学校科研项目(KY2015ZD103和KY2015LX341)

摘　　要：研究一类新的弱奇异非线性迭代积分不等式,运用放大技巧、积分微分技巧、变量替换技巧、反函数技巧、常量与变量的辩证关系以及离散詹森不等式,给出不等式中未知函数的估计;推广参考文献中相应的结果;最后,用所得结果给出相应奇异积分方程解的估计.In this paper,we establish a class of new nonlinear integral inequality which consists of iterated integral.Estimation of the unknown functions in the inequality is given by change of variable,amplification method,integral differential technique,the dialectical relationship between constants and variables,discrete Jensen inequality,inverse function technique,and Gamma function.Our results generalize the corresponding results in the references.Finally,estimation of solutions of corresponding weakly singular nonlinear iterated integral equations is given by the derived results.

关 键 词：积分不等式 弱奇异积分核 迭代积分 分析技巧 估计 

分 类 号：O175.5[理学—数学]