IJPAM: Volume 79, No. 4 (2012)

BOUNDED POSITIVE SOLUTIONS OF SECOND ORDER
NONLINEAR NEUTRAL DIFFERENCE EQUATIONS

Jinbiao Hao$^1$, Shin Min Kang$^2$
$^1$Department of Mathematics
Liaoning Normal University
Dalian, Liaoning 116029, P.R. CHINA
$^2$Department of Mathematics and RINS
Gyeongsang National University
Jinju, 660-701, KOREA


Abstract. This paper is considered with the second order nonlinear neutral difference equations

\begin{displaymath} \Delta^2(y_n\pm y_{n-\tau})+f(n+1,y_{n+1-\sigma})=0,\quad\forall n\ge n_0. \end{displaymath}

The existence results of bounded positive solutions for the equations are proved by using the Rothe fixed point theorem. Two nontrivial examples are included.

Received: July 4, 2012

AMS Subject Classification: 39A10, 39A20

Key Words and Phrases: second order nonlinear neutral difference equation, bounded positive solution, Rothe 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: 79
Issue: 4