一类非线性弱奇异多重积分不等式中未知函数的估计及其应用

Estimation of unknown function of a class of nonlinear weakly singular triple integral inequality and its application

研究了一类非线性弱奇异多重积分不等式,被积函数中含有积分变量,积分项外包含了非常数项,利用离散Jensen不等式、Cauchy-Schwarz积分不等式、变量替换技巧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.最后举例说明所得结果可以用来研究弱奇异积分方程解的定性性质.

A class of nonlinear weakly singular multiple integral inequalities are investigated in this paper, which include a nonconstant term outside the integrals, and integral variable is included in the integrands in the integral inequality. The upper bounds of the embedded unknown functions are estimated explicitly by adopting some analysis techniques, such as discrete Jensen inequality, Cauchy-Schwarz integral inequality, the techniques of change of variable, and the method of amplification. The derived results can be applied in the study of qualitative properties of solutions of multiple fractional integral equations.