Department of Mathematics, University of Pannonia, P.O. Box 158, 8201 Veszprém, Hungary
Copyright © 2010 B. Krasznai et al. This is an open access article distributed under the
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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.