Some nonlinear Gronwall–Bellman type retarded integral inequalities with power and their applications

摘要

The purpose of this paper is to establish some new retarded integral inequalities of Gronwall-Bellman type, which generalizes some known integral inequalities. We use two lemmas to simplify the complex inequalities and give an upper bound estimation of the unknown function. The inequalities given here can be used in the analysis of the qualitative properties of certain classes of differential equations and integral equations. We apply our results to the boundedness of the solutions of integral equations and differential system.