Oscillation of a Nonlinear Difference Equation of Power Type | OMICS International | Abstract
ISSN: 2168-9679

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## Oscillation of a Nonlinear Difference Equation of Power Type

Bakery AA*

Department of Mathematics, Faculty of Science and Arts, University of Jeddah, Saudi Arabia

*Corresponding Author:
Bakery AA
Department of Mathematics
Faculty of Science and Arts
P.O. Box 355, Khulais 21921
University of Jeddah (U j), Saudi Arabia
Tel: 966126952000
E-mail: [email protected]

Received: October 27, 2015; Accepted: November 09, 2015; Published: November 13, 2015

Citation: Bakery AA (2015) Oscillation of a Nonlinear Difference Equation of Power Type. J Appl Computat Math 4:270. doi:10.4172/2168-9679.1000270

Copyright: © 2015 Bakery AA. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

### Abstract

We give in this work the sufficient conditions on the positive solutions of the difference equation 8 1 1 n n n n x x x x α − + = + , n=0,1,…., where α ≥ 0 and s > 0 with arbitrary positive initials x-1; x0 to be bounded and the equilibrium point to be globally asymptotically stable. Finally we present the condition for which every positive solution converges to a prime two periodic solution. We have given a non-oscillatory positive solution which converges to the equilibrium point.

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