On Regulated Solutions of Impulsive Differential Equations with Variable Times

Abstract

In this paper we investigate the unified theory for solutions of differential equations without impulses and with impulses, even at variable times, allowing the presence of beating phenomena, in the space of regulated functions. One of the aims of the paper is to give sufficient conditions to ensure that a regulated solution of an impulsive problem is globally defined.

Keywords

• regulated function
• solution set
• discontinuous function
• impulsive problem with variable times