Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 195916, 14 pages
doi:10.1155/2010/195916
Research Article

Fixed Points and Stability in Nonlinear Equations with Variable Delays

Liming Ding,1,2 Xiang Li,1 and Zhixiang Li1

1Department of Mathematics and System Science, College of Science, National University of Defence Technology, Changsha 410073, China
2Air Force Radar Academy, Wuhan 430010, China

Received 9 July 2010; Accepted 18 October 2010

Academic Editor: Hichem Ben-El-Mechaiekh

Copyright © 2010 Liming Ding et al. 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 consider two nonlinear scalar delay differential equations with variable delays and give some new conditions for the boundedness and stability by means of the contraction mapping principle. We obtain the differences of the two equations about the stability of the zero solution. Previous results are improved and generalized. An example is given to illustrate our theory.