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International Journal of Mathematics and Mathematical Sciences

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

E. Thandapani, S. Lourdu Marian, John R. Graef, "Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations", International Journal of Mathematics and Mathematical Sciences, vol. 27, Article ID 415039, 8 pages, 2001. https://doi.org/10.1155/S0161171201006172

Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations

E. Thandapani,1 S. Lourdu Marian,1 and John R. Graef2

1Department of Mathematics, Periyar University, India

2Department of Mathematics, University of Tennessee at Chattanooga, USA

Received10 Nov 2000

Abstract

The authors consider the mth order nonlinear difference equations of the form Dmyn+qnf(yσ(n))=ei, where m≥1, n∈ℕ={0,1,2,…}, ani>0 for i=1,2,…,m−1, anm≡1, D0yn=yn, Diyn=aniΔDi−1yn, i=1,2,…,m, σ(n)→∞ as n→∞, and f:ℝ→ℝ is continuous with uf(u)>0 for u≠0. They give sufficient conditions to ensure that all bounded nonoscillatory solutions tend to zero as n→∞ without assuming that ∑n=0∞1/ani=∞, i=1,2,…,m−1, {qn} is positive, or en≡0 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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