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Advances in Difference Equations

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Research Article
Open Access

A classification scheme for nonoscillatory solutions of a higher order neutral difference equation

  • Zhi-qiang Zhu1,
  • Gen-qiang Wang1 and
  • Sui Sun Cheng2
Advances in Difference Equations20062006:047654

https://doi.org/10.1155/ADE/2006/47654

©  Zhi-qiang Zhu et al. 2006

Received: 25 May 2005

Accepted: 28 September 2005

Published: 23 February 2006

Abstract

Nonoscillatory solutions of a nonlinear neutral type higher order difference equations are classified by means of their asymptotic behaviors. By means of the Kranoselskii's fixed point theorem, existence criteria are then provided for justification of such classification.

Keywords

Differential EquationPartial Differential EquationOrdinary Differential EquationFunctional AnalysisAsymptotic Behavior

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Authors’ Affiliations

(1)
Department of Computer Science, Guangdong Polytechnic Normal University, Guangzhou, China
(2)
Department of Mathematics, Tsing Hua University, Hsinchu, China

References

  1. Agarwal RP: Difference Equations and Inequalities. Theory, Methods, and Applications, Monographs and Textbooks in Pure and Applied Mathematics. Volume 155. Marcel Dekker, New York; 1992:xiv+777.Google Scholar
  2. Chen YS: Asymptotic behavior of nonoscillatory solutions of higher order neutral delay differential equations. Annals of Differential Equations 1993,9(3):270–286.MathSciNetMATHGoogle Scholar
  3. Cheng SS: Partial Difference Equations. Taylor & Francis, London; 2003.View ArticleMATHGoogle Scholar
  4. Cheng SS, Zhang G, Li W-T: On a higher order neutral difference equation. In Mathematical Analysis and Applications. Edited by: Rassias ThM. Hadronic Press, Florida; 2000:37–64.Google Scholar
  5. He XZ: Oscillatory and asymptotic behaviour of second order nonlinear difference equations. Journal of Mathematical Analysis and Applications 1993,175(2):482–498. 10.1006/jmaa.1993.1186MathSciNetView ArticleMATHGoogle Scholar
  6. Lalli BS: Oscillation theorems for neutral difference equations. Advances in difference equations. Computers & Mathematics with Applications 1994,28(1–3):191–202.MathSciNetView ArticleMATHGoogle Scholar
  7. Li W-T, Cheng SS, Zhang G: A classification scheme for nonoscillatory solutions of a higher order neutral nonlinear difference equation. Journal of the Australian Mathematical Society. Series A 1999,67(1):122–142. 10.1017/S1446788700000902MathSciNetView ArticleMATHGoogle Scholar
  8. Tang X, Yan J: Oscillation and nonoscillation of an odd-order nonlinear neutral difference equation. Functional Differential Equations 2000,7(1–2):157–166 (2001).MathSciNetMATHGoogle Scholar
  9. Zhang G, Cheng SS: Oscillation criteria for a neutral difference equation with delay. Applied Mathematics Letters 1995,8(3):13–17. 10.1016/0893-9659(95)00022-IMathSciNetView ArticleMATHGoogle Scholar
  10. Zhang B, Sun YJ: Classification of nonoscillatory solutions of a higher order neutral difference equation. Journal of Difference Equations and Applications 2002,8(11):937–955. 10.1080/1023619021000048841MathSciNetView ArticleMATHGoogle Scholar
  11. Zhang BG, Yang B: Oscillation in higher-order nonlinear difference equations. Chinese Annals of Mathematics. Series A 1999,20(1):71–80.MathSciNetMATHGoogle Scholar

Copyright

© Zhi-qiang Zhu et al. 2006

This article is published under license to BioMed Central Ltd. 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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