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

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.

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References

  1. 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. 2.

    Chen YS: Asymptotic behavior of nonoscillatory solutions of higher order neutral delay differential equations. Annals of Differential Equations 1993,9(3):270–286.

    MathSciNet  MATH  Google Scholar 

  3. 3.

    Cheng SS: Partial Difference Equations. Taylor & Francis, London; 2003.

    Google Scholar 

  4. 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. 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.1993.1186

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Lalli BS: Oscillation theorems for neutral difference equations. Advances in difference equations. Computers & Mathematics with Applications 1994,28(1–3):191–202.

    MathSciNet  Article  MATH  Google Scholar 

  7. 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/S1446788700000902

    MathSciNet  Article  MATH  Google Scholar 

  8. 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).

    MathSciNet  MATH  Google Scholar 

  9. 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-I

    MathSciNet  Article  MATH  Google Scholar 

  10. 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. 10.1080/1023619021000048841

    MathSciNet  Article  MATH  Google Scholar 

  11. 11.

    Zhang BG, Yang B: Oscillation in higher-order nonlinear difference equations. Chinese Annals of Mathematics. Series A 1999,20(1):71–80.

    MathSciNet  MATH  Google Scholar 

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Correspondence to Zhi-qiang Zhu.

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Zhu, Zq., Wang, Gq. & Cheng, S.S. A classification scheme for nonoscillatory solutions of a higher order neutral difference equation. Adv Differ Equ 2006, 047654 (2006). https://doi.org/10.1155/ADE/2006/47654

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Asymptotic Behavior
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