二元积分不等式的若干推广及应用

Generalizations of Integral Inequalities with Two Variables and their Applications

摘要:

在本文中，我们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，通过将不等式中的函数单调化和积分号外函数作常量化的方法, 给出这类不等式中未知函数的估计, 并且以推论形式给出相应的一元积分不等式中未知函数的解的估计. 最后, 利用该估计证明了一类积分方程和一类微分方程的解的有界性.

Abstract:

In this paper, we discuss a retarded nonlinear integral inequality with two variables. By 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 that the solutions of two types of equations, one are integral equations and the other differential equations, are bounded.