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

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(h1(t)),…,x(hl(t)))](i)+f(t,x(f1(t)),…,x(fl(t)))=g(t), for all t≥t0. Using the Banach fixed point theorem, we establish the existence results of uncountably many positive...

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Bibliographic Details
Main Authors: Zeqing Liu, Ling Guan, Sunhong Lee, Shin Min Kang
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/165382
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Summary: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(h1(t)),…,x(hl(t)))](i)+f(t,x(f1(t)),…,x(fl(t)))=g(t), for all t≥t0. 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.
ISSN:1085-3375
1687-0409