Open Access
2013 Existence and Iterative Algorithms of Positive Solutions for a Higher Order Nonlinear Neutral Delay Differential Equation
Zeqing Liu, Ling Guan, Sunhong Lee, Shin Min Kang
Abstr. Appl. Anal. 2013(SI21): 1-28 (2013). DOI: 10.1155/2013/165382

Abstract

This paper is concerned with the higher order nonlinear neutral delay differential equation [ a ( t ) ( x ( t ) + b ( t ) x ( t - τ ) ) ( m ) ] ( n - m ) + [ h ( t , x ( h 1 ( t ) ) , , x ( h l ( t ) ) ) ] ( i ) + f ( t , x ( f 1 ( t ) ) , , x ( f l ( t ) ) ) = g ( t ) , for all t t 0 . 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.

Citation

Download Citation

Zeqing Liu. Ling Guan. Sunhong Lee. Shin Min Kang. "Existence and Iterative Algorithms of Positive Solutions for a Higher Order Nonlinear Neutral Delay Differential Equation." Abstr. Appl. Anal. 2013 (SI21) 1 - 28, 2013. https://doi.org/10.1155/2013/165382

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1266.65114
MathSciNet: MR3035205
Digital Object Identifier: 10.1155/2013/165382

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI21 • 2013
Back to Top