二元积分不等式的若干推广

Generalizations of integral inequalities with two variables

本文主要研究一类具有时滞的二元非线性积分不等式.在不要求已知函数的单调性和可微性的条件下,本文通过将不等式中的函数单调化和积分号外函数常量化的方法给出了这类不等式中未知函数的估计,并以推论形式给出相应一元积分不等式中未知函数的解的估计.最后,本文利用该估计证明了一类积分方程和一类微分方程解的有界性.

In this paper,we consider a retarded nonlinear integral inequality with two variables.Using the techniques of monotonization and reducing the function outside the integral to constant,we give an estimation of the unknown function in the inequality.Finally,by applying our result we prove boundedness of the solutions for two types of equations.