Abstract and Applied Analysis
Volume 2013 (2013), Article ID 165382, 28 pages
http://dx.doi.org/10.1155/2013/165382
Research Article

Existence and Iterative Algorithms of Positive Solutions for a Higher Order Nonlinear Neutral Delay Differential Equation

Zeqing Liu,1 Ling Guan,1 Sunhong Lee,2 and Shin Min Kang2

1Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, China
2Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

Received 23 October 2012; Accepted 10 December 2012

Academic Editor: Jifeng Chu

Copyright © 2013 Zeqing Liu 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

This paper is concerned with the higher order nonlinear neutral delay differential equation for all . Using the Banach fixed point theorem, we establish the existence results of uncountably many positive solutions for the equation, construct Mann iterative sequences for approximating these positive solutions, and discuss error estimates between the approximate solutions and the positive solutions. Nine examples are included to dwell upon the importance and advantages of our results.