On the Existence of Extremal Solutions for Impulsive Differential Equations with Variable Time

In this paper we continue the study of the existence of extremal solutions for scalar impulsive differential equations (IDE) with variable time begun in [1,6]. In [1,6] we considered the problem starting with the extremal solutions of the associated differential equation without impulses. Here, however, we establish the existence of such solutions directly using Peano’s method.