Skip to main content
SpringerLink
Log in

Oscillatory behavior of the second-order nonlinear neutral difference equations

  • Published:
Korean Journal of Computational & Applied Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we consider the oscillation of the second-order neutral difference equation

$$\Delta ^2 \left( {x_n - px_{n - \tau } } \right) + q_n f\left( {x_{n - \sigma _n } } \right) = 0$$

as well as the oscillatory behavior of the corresponding ordinary difference equation

$$\Delta ^2 z_n + q_n f\left( {R\left( {n,\lambda } \right)z_n } \right) = 0$$

.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P.J.Y.Wong and R.P.Agarwal,Oscillation Theorems and Existence of Positive Monotone Solutions for Second Order Nonlinear Difference Equations. Math.Comput.Modelling, Vol 21, No 9. (1995).

  2. Z. Szafranski and B. Szmanda.Oscillation Theorems for Some Nonlinear Difference Equations, Appl.Math.Comput. 83:43–52 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  3. E. Thandapni and P. Sanadapani,On the Asymptotic and Oscillatory Behavior of second order Nonlinear Neutral Difference Equations. Indian J.pure.Appl.Math. 26 (19), 1995.

  4. E.Thandapni and R. Arul,Oscillation Properties of Second Order Nonlinear Neutral Delay Difference Equations. Indian J.Pure.Appl.Math.28 (12), 1997.

  5. Zhenguo Zhang and Qiaoluan Li,Oscillation Theorems for Second Order Advanced Functional Difference Equation. Computers Math.Appl, Vol 36, No 6. (1988).

  6. Zhenguo Zhang and Jinlian Zhang Zhenguo Zhang and Jinlian Zhang,Oscillation Criteria for Second Order Functional Difference Equations with “summation Small” coefficient. Computers Math.Appl, 38 (1999), 25–31.

    Article  MATH  Google Scholar 

  7. R.P.Agarwal, M.M.S.Manael and E.Thandapni,Oscillatory and Nonoscillatory Behavior of Second-Order Neutral Delay Difference Equations. Appl.Math.lett. Vol.10, No.2 (1997).

  8. Dteudorme.J,Foundations of Modern Analysis. Academic Press, Vol. 11 (1969), Vol 2 (1972).

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Information of Science, HeBei Normal University, 050016, Shijiazhuang, P.R. China

    Zhenguo Zhang, Wenlei Dong & Bi Ping

Authors
  1. Zhenguo Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenlei Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bi Ping
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhenguo Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Z., Dong, W. & Ping, B. Oscillatory behavior of the second-order nonlinear neutral difference equations. Korean J. Comput. & Appl. Math. 8, 111–128 (2001). https://doi.org/10.1007/BF03011626

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03011626

AMS Mathematics Subject Classification

Key words and phrases

Search

Navigation