Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 37195, 10 pages
doi:10.1155/JIA/2006/37195

Exponential stability in a scalar functional differential equation

Eduardo Liz1 and Mihály Pituk2

1Departamento de Matemática Aplicada II, ETSI Telecomunicación, Universidade de Vigo, Campus Marcosende, Vigo 36280, Spain
2Department of Mathematics and Computing, University of Veszprém, P.O. Box 158, Veszprém 8201, Hungary

Received 21 March 2006; Revised 16 August 2006; Accepted 21 September 2006

Copyright © 2006 Eduardo Liz and Mihály Pituk. 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 establish a criterion for the global exponential stability of the zero solution of the scalar retarded functional differential equation x'(t)=L(xt)+g(t,xt) whose linear part y'(t)=L(yt) generates a monotone semiflow on the phase space C=C([−r,0],ℝ) with respect to the exponential ordering, and the nonlinearity g has at most linear growth.