International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2001 / Article

Open Access

Volume 27 |Article ID 415039 | 8 pages | https://doi.org/10.1155/S0161171201006172

Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations

Received10 Nov 2000

Abstract

The authors consider the mth order nonlinear difference equations of the form Dmyn+qnf(yσ(n))=ei, where m1, n={0,1,2,}, ani>0 for i=1,2,,m1, anm1, D0yn=yn, Diyn=aniΔDi1yn, i=1,2,,m, σ(n) as n, and f: is continuous with uf(u)>0 for u0. They give sufficient conditions to ensure that all bounded nonoscillatory solutions tend to zero as n without assuming that n=01/ani=, i=1,2,,m1, {qn} is positive, or en0 as is often required. If {qn} is positive, they prove another such result for all nonoscillatory solutions.

Copyright © 2001 Hindawi Publishing Corporation. 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.


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