Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 618058, 13 pages
http://dx.doi.org/10.1155/2012/618058
Research Article

Existence for Eventually Positive Solutions of High-Order Nonlinear Neutral Differential Equations with Distributed Delay

Huanhuan Zhao,1 Youjun Liu,1 and Jurang Yan2

1College of Mathematics and Computer Sciences, Shanxi Datong University, Datong, Shanxi 037009, China
2School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China

Received 14 February 2012; Accepted 12 March 2012

Academic Editor: Mingshu Peng

Copyright © 2012 Huanhuan Zhao 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 the existence for eventually positive solutions of high-order nonlinear neutral differential equations with distributed delay. We use Lebesgue's dominated convergence theorem to obtain new necessary and sufficient condition for the existence of eventually positive solutions.