Abstract and Applied Analysis
Volume 2011 (2011), Article ID 969276, 29 pages
http://dx.doi.org/10.1155/2011/969276
Research Article

Neutral Operator and Neutral Differential Equation

Jingli Ren,1 Zhibo Cheng,1 and Stefan Siegmund2

1Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China
2Department of Mathematics, Dresden University of Technology, 01062 Dresden, Germany

Received 22 March 2011; Accepted 15 June 2011

Academic Editor: Allan C. Peterson

Copyright © 2011 Jingli Ren 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

In this paper, we discuss the properties of the neutral operator (Ax)(t)=x(t)−cx(t−δ(t)), and by applying coincidence degree theory and fixed point index theory, we obtain sufficient conditions for the existence, multiplicity, and nonexistence of (positive) periodic solutions to two kinds of second-order differential equations with the prescribed neutral operator.