一类非连续函数的 Bellman-Bihari 型积分不等式的推广及应用

本文研究了一类具有时滞的非连续函数的Bellman-Bihari型非线性积分不等式,在Gallo和Piccirillo的结果的基础上,增加了二元函数项,放弃对函数的单调性和可分离性要求.通过将不等式中的函数单调化和积分号外的函数作常量化,作者给出了不等式中未知函数的估计,进而将所得的不等式的估计用于研究一类脉冲微分方程的解的估计.

On some generalizations integral inequalities of Bellman-Bihari type for discontinuous functions and their applications

In this paper some nonlinear integral inequalities of Bellman Bihari type for discontinuous function are considered. On the basis of Gallo and Piccirillo's result, a term of function of two variables is added and require neither the monotonicity nor the separability of given functions. Estimations of unknown functions in the inequalities are given by techniques of the monotonization and a reduction to constant for the term outside the integral. finally, the result is applied to discuss estimates of solution for the impulsive differential equation.