Positive Solutions and Mann Iterations of a Fourth Order Nonlinear Neutral Delay Differential Equation-Reference-Cited by-同舟云学术

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

Published:2014 Issue: Volume:2014 Page:1-22
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Liu Zeqing¹^ORCID,Zhu Jingjing²,Ume Jeong Sheok³,Kang Shin Min⁴^ORCID

Affiliation:

1. Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, China

2. Dalian No. 39 Middle School Dalian, Liaoning 116001, China

3. Department of Mathematics, Changwon National University, Changwon 641-773, Republic of Korea

4. Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

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.

Funder

Educational Department of Liaoning Province

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/105719.pdf

Reference13 articles.

1. Oscillation/Nonoscillation Criteria for Linear Second Order Differential Equations

2. Oscillation and Nonoscillation for Second Order Linear Differential Equations

3. Existence of Nonoscillatory Solution of Second Order Linear Neutral Delay Equation

4. Oscillation of second-order nonlinear neutral differential equations