T. Ghrissi and M. A. Hammamiy
On Some Retarded Integral Inequalities of Gronwall Type: Application to Integral and Differential Equations
Dynamic Systems and Applications 32 (2023)  33-54

https://doi.org/10.46719/dsa2023.32.03

ABSTRACT.
We present in this paper some new inequalities of Gronwall-type. As an application, we consider the problem of asymptotic behaviors of a class of retarded Volterra equations. We establish bounds on the solutions and, by means of examples, we show and discuss the usefulness of our results in investigating the asymptotic stability of the solutions. Moreover, we study via integral inequalities the stability of certain dynamical systems.

AMS (MOS) Subject Classification. 34L10, 34B24, 47E05.

Key Words and Phrases. Integral inequalities of Gronwall type, integral equations, differential equations, stability.