Fixed Point Theory and Applications
Volume 2005 (2005), Issue 1, Pages 35-46

Fixed points, stability, and harmless perturbations

T. A. Burton

Northwest Research Institute, 732 Caroline Street, Port Angeles 98362, WA, USA

Received 14 July 2004; Revised 11 September 2004

Copyright © 2005 T. A. Burton. 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.


Much has been written about systems in which each constant is a solution and each solution approaches a constant. It is a small step to conjecture that functions promoting such behavior constitute harmless perturbations of stable equations. That idea leads to a new way of avoiding delay terms in a functional-differential equation. In this paper we use fixed point theory to show that such a conjecture is valid for a set of classical equations.