Abstract:
Gronwall-Bellman inequalities and their various generalizations that give explicit bounds on unknown functions provide a very useful and important device in the study of many qualitative properties of solutions of differential equations, integral equations and integrodifferential equations. The purpose of this work is to give an exposition of some classical
and modern results about integral inequalities, and establish some new nonlinear integral inequalities with delay in two independent variables, which generalize some known inequalities recently obtained. These results can be used as handy tools to study the boundedness of solutions of Volterra integral equations. Applications are given to illustrate how our results can be applied to study the boundedness of the solutions of certain Volterra equations. The research on this topic is also large and continues until now, the impressive number of publications on this subject testifies to this.
