Journal of Applied Mathematics and Stochastic Analysis 
Volume 10 (1997), Issue 1, Pages 89-94
doi:10.1155/S1048953397000099

Integral inequalities of Gronwall type for piecewise continuous functions

Drumi D. Bainov1 and Snezhana G. Hristova2

 1Medical University of Sofia, P.O. Box 45, Sofia 1504, Bulgaria
2Plovdiv University “Paissii Hilendarski”, Tsar Asen Str., 24, Plovdiv 4000, Bulgaria
Received 1 March 1995; Revised 1 March 1996

Abstract

In this paper we generalize the integral inequality of Gronwall and study the continuous dependence of the solution of the initial value problem for nonlinear impulsive integro-differential equations of Volterra type on the initial conditions.