Asymptotic formulae for solutions to impulsive differential equations with piecewise constant argument of generalized type

Abstract

In this article we give some asymptotic formulae for impulsive differential system with piecewise constant argument of generalized type (abbreviated IDEPCAG). These formulae are based on certain integrability conditions, by means of a Gronwall-Bellman type inequality and the Banach's fixed point theorem. Also, we study the existence of an asymptotic equilibrium of nonlinear and semilinear IDEPCAG systems. We present examples that illustrate our the results.

Keywords

• Piecewise constant arguments
• stability of solutions
• Gronwall's inequality
• asymptotic equivalence
• impulsive differential equations