一类二重积分不等式中未知函数的估计

基金项目:

国家自然科学基金项目;国家自然科学基金项目;广西自然科学基金项目

详细信息

Estimation of Unknown Function of a Class of Double Integral Inequalities

摘要: 利用变量替换技巧、放大技巧和反函数技巧等方法, 研究了一类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的非线性二重积分不等式，给出该类不等式中未知函数的显上界估计，并举例说明所得结果可以用来研究微分-积分方程解的估计.
- 非线性积分不等式 /
- 含有未知导函数的二重积分 /
- 微分-积分方程 /
- 显式估计
Abstract: A class of nonlinear double integral inequalities is studied, which includes an unknown function and its derivative function in integrand function, and a nonconstant factor outside integral sign. The upper bound of the unknown function in the integro-differential inequality is estimated explicitly using the techniques of change of variable, the method of amplification, and inverse function technique. The derived results can be applied in the study of the explicit upper bounds of solutions of a class of integro-differential equations.
- nonlinear integral inequality /
- double integral with unknown derivative function /
- integro-differential equation /
-  explicit estimation