IJPAM: Volume 80, No. 3 (2012)
SOLUTIONS FOR A THIRD ORDER NEUTRAL
DELAY DIFFERENTIAL EQUATION
Department of Mathematics
Liaoning Normal University
Dalian, Liaoning, 116029, P.R. CHINA
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