Electron. J. Differential Equations, Vol. 2019 (2019), No. 40, pp. 1-22.

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

Samuel Castillo, Manuel Pinto, Ricardo Torres

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.

Show me the PDF file (406 KB), TEX file for this article.

Samuel Castillo
Grupo de Investigación de Sistemas Dinámicos y aplicaciones (GISDA)
Departamento de Matemáticas, Facultad de Ciencias
Universidad del Bío-Bío
Concepción, Chile
email: scastill@ubiobio.cl
Manuel Pinto
Departamento de Matemáticas
Facultad de Ciencias, Universidad de Chile
Santiago, Chile
email: pintoj@uchile.cl, pintoj.uchile@gmail.com
Ricardo Torres
Instituto de Ciencias Físicas y Matemáticas
Facultad de Ciencias, Universidad Austral de Chile
Campus Isla Teja, Valdivia, Chile
email: ricardo.torres@uach.cl, ricardotorresn@gmail.com

Return to the EJDE web page