Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 40, pp. 1-22.

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

Authors: Samuel Castillo (Univ. del Bio-Bio,  Concepcion, Chile)
         Manuel Pinto  (Univ. de Chile, Santiago, Chile)
         Ricardo Torres (Univ. Austral de Chile, Valdivia, Chile)
 
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.


Submitted August 25, 2018. Published March 12, 2019.
Math Subject Classifications: 34A38, 34A37, 34A36, 34C41, 34D05, 34D20.
Key Words: Piecewise constant arguments; stability of solutions;
           Gronwall's inequality; asymptotic equivalence; 
           impulsive differential equations.