IJPAM: Volume 80, No. 3 (2012)

EXISTENCE AND ITERATIVE ALGORITHMS OF POSITIVE
SOLUTIONS FOR A THIRD ORDER NEUTRAL
DELAY DIFFERENTIAL EQUATION

Zeqing Liu$^1$, Ling Guan$^2$, Shin Min Kang$^3$
$^{1,2}$Department of Mathematics
Liaoning Normal University
Dalian, Liaoning, 116029, P.R. CHINA
$^{3}$Department of Mathematics and RINS
Gyeongsang National University
Jinju 660-701, KOREA


Abstract. This paper deals with a third order nonlinear neutral delay differential equation. By using the Banach fixed point theorem, we establish three existence results of uncountably many bounded positive solutions for the equation, construct the Mann iterative schemes for approximating these bounded positive solutions and discuss error estimates between the approximate solutions and the bounded positive solutions. Three examples are given to explain the results in this paper.

Received: September 19, 2012

AMS Subject Classification: 34K40

Key Words and Phrases: third order neutral delay differential equation, uncountably many bounded positive solutions, Banach fixed point theorem, Mann iterative scheme

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 3