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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 105719, 22 pages
http://dx.doi.org/10.1155/2014/105719
Research Article

Positive Solutions and Mann Iterations of a Fourth Order Nonlinear Neutral Delay Differential Equation

1Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, China
2Dalian No. 39 Middle School Dalian, Liaoning 116001, China
3Department of Mathematics, Changwon National University, Changwon 641-773, Republic of Korea
4Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

Received 16 December 2013; Accepted 20 February 2014; Published 29 May 2014

Academic Editor: Allan Peterson

Copyright © 2014 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 deals with a fourth order nonlinear neutral delay differential equation. By using the Banach fixed point theorem, we establish the existence of uncountably many bounded positive solutions for the equation, construct several Mann iterative sequences with mixed errors for approximating these positive solutions, and discuss some error estimates between the approximate solutions and these positive solutions. Seven nontrivial examples are given.