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International Journal of Mathematics and Mathematical Sciences
Volume 25, Issue 12, Pages 787-801
http://dx.doi.org/10.1155/S016117120100429X

Ergodicity and asymptotically almost periodic solutions of some differential equations

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 20 December 1999

Copyright © 2001 Hindawi Publishing Corporation. 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

Using ergodicity of functions, we prove the existence and uniqueness of (asymptotically) almost periodic solution for some nonlinear differential equations. As a consequence, we generalize a Massera’s result. A counterexample is given to show that the ergodic condition cannot be dropped.