Advances in Difference Equations
Volume 2010 (2010), Article ID 973432, 16 pages
doi:10.1155/2010/973432
Research Article

Positive Decreasing Solutions of Higher-Order Nonlinear Difference Equations

B. Krasznai, I. Győri, and M. Pituk

Department of Mathematics, University of Pannonia, P.O. Box 158, 8201 Veszprém, Hungary

Received 23 December 2009; Accepted 13 May 2010

Academic Editor: Ağacik Zafer

Copyright © 2010 B. Krasznai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It is shown that the decay rates of the positive, monotone decreasing solutions approaching the zero equilibrium of higher-order nonlinear difference equations are related to the positive characteristic values of the corresponding linearized equation. If the nonlinearity is sufficiently smooth, this result yields an asymptotic formula for the positive, monotone decreasing solutions.