Fixed Point Theory and Applications 
Volume 2005 (2005), Issue 1, Pages 35-46
doi:10.1155/FPTA.2005.35

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

Abstract

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.