International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 10, Pages 609-619
doi:10.1155/S0161171201006263

Ergodic type solutions of differential equations with piecewise constant arguments

Ana Isabel Alonso1 and Jialin Hong2

1Departamento de Matemática Aplicada a la Ingeniería, Paseo del Cauce s/n. 47011, Universidad de Valladolid, Spain
2Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing 100080, China

Received 27 November 2000

Copyright © 2001 Ana Isabel Alonso and Jialin Hong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We summarize the conditions discovered for the existence of new ergodic type solutions (asymptotically almost periodic, pseudo almost periodic, …) of differential equations with piecewise constant arguments. Their existence is characterized by introducing a new tool, the ergodic sequences.