Journal of Applied Mathematics and Stochastic Analysis
Volume 6 (1993), Issue 1, Pages 35-48
Nonlinear impulsive Volterra integral equations in Banach spaces and applications
Shangdong University, Jinan, Department of Mathematics, Shangdong 250100, China
Received 1 November 1992; Revised 1 February 1993
Copyright © 1993 Dajun Guo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper, we first extend results on the existence of maximal
solutions for nonlinear Volterra integral equations in Banach spaces to
impulsive Volterra integral equations. Then, we give some applications
to initial value problems for first order impulsive differential equations in
Banach spaces. The results are demonstrated by means of an example of
an infinite system for impulsive differential equations.