IJPAM: Volume 77, No. 1 (2012)

BOUNDED POSITIVE SOLUTIONS FOR A SECOND
ORDER NEUTRAL DELAY DIFFERENCE EQUATION

Lijun He$^1$, Shin Min Kang$^2$, Chahn Yong Jung$^3$
$^1$Department of Physics and Mathematics
Kunming Medical College
Kunming, Yunnan 650031, P.R. CHINA
$^2$Department of Mathematics and RINS
Gyeongsang National University
Jinju, 660-701, KOREA
$^3$Department of Business Administration
Gyeongsang National University
Jinju, 660-701, KOREA


Abstract. This paper studies solvability of the second order neutral delay difference equation

\begin{displaymath} \Delta^2(x_n+bx_{n-\tau}) +f(n,x_{n-c_{n}},x_{n-d_{n}})=0, \quad n\ge n_0. \end{displaymath}

Using the Banach fixed point theorem, we show the existence of a bounded positive solution for the difference equation. Three examples are also included.

Received: February 2, 2012

AMS Subject Classification: 39A10

Key Words and Phrases: second order neutral delay difference equation, bounded positive solution, Banach fixed point theorem

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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: 77
Issue: 1