Skip to main content
SpringerLink
Log in

Oscillatory and asymptotic behavior of solutions of higher order damped nonlinear difference equations

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

The asymptotic and oscillatory behavior of solutions of mth order damped nonlinear difference equation of the form \(\Delta (a_n \Delta ^{m - 1} y_n ) + p_n \Delta ^{m - 1} y_n + q_n f(y_{\sigma (n + m - 1)} ) = 0\) where m is even, is studied. Examples are included to illustrate the results.

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. R.P. Agarwal: Difference Equations and Inequalities. Marcel Dekker, New York, 1992.

    Google Scholar 

  2. R.P. Agarwal: Properties of solutions of higher order nonlinear difference equations I. An. Univ. AI.I. Cuza. Iasi. 31 (1985), 165-172.

    Google Scholar 

  3. R.P. Agarwal: Properties of solutions of higher order nonlinear difference equations II. An. Univ. AI.I. Cuza. Iasi 29 (1983), 85-96.

    Google Scholar 

  4. S.R. Grace and B.S. Lalli: Oscillation theorems for n-th order delay differential equations. J. Math. Anal. Appl. 91 (1983), 342-366.

    Google Scholar 

  5. S.R. Grace and B.S. Lalli: Oscillation theorems for damped differential equations of even order with deviating arguments. SIAM. J. Math. Anal. 15 (1984), 308-316.

    Google Scholar 

  6. J.W. Hooker and W.T. Patula: A second order nonlinear difference equation: Oscillation and asymptotic behavior. J. Math. Anal. Appl. 91 (1983), 9-29.

    Google Scholar 

  7. M.R.S. Kulenovic and M. Budincevic: Asymptotic analysis of nonlinear second order difference equations. Anal. Sti. Univ. Iasi. 30 (1984), 39-52.

    Google Scholar 

  8. V. Lakshmikantham and D. Trigiante: Theory of Difference Equations: Numerical Methods and Applications. Academic Press, New York, 1988.

    Google Scholar 

  9. J. Popenda: Oscillation and nonoscillation theorems for second order difference equations. J. Math. Anal. Appl. 123 (1987), 34-38.

    Google Scholar 

  10. E. Thandapani: Asymptotic and oscillatory behavior of solutions of nonlinear second order difference equations. Indian. J. Pure. Appl. Math. 24 (1993), 365-372.

    Google Scholar 

  11. E. Thandapani: Oscillation theorems for second order damped nonlinear difference equations. Czechoslovak Math. J. 45(120) (1995), 327-335.

    Google Scholar 

  12. E. Thandapani, P. Sundaram and B.S. Lalli: Oscillation theorems for higher order nonlinear delay difference equations. Computers Math. Applic. 32 (1996), 111-117.

    Google Scholar 

  13. E. Thandapani, P. Sundaram, J.R. Graef, A. Miciano and P.W. Spikes: Classification of nonoscillatory solutions of higher order neutral type difference equations. Arch. Math. (Brno) 31 (1995), 263-277.

    Google Scholar 

  14. E. Thandapani and P. Sundaram: Oscillation theorems for some even order nonlinear difference equations. J. Nonlinear Diff. Eqn. 4 (1996). To appear.

  15. P.J.Y. Wong and R.P. Agarwal: Oscillation theorems and existence of positive monotone solutions for second order non linear difference equations. Math. Comp. Modelling 21 (1995), 63-84.

    Google Scholar 

  16. P.J.Y. Wong and R.P. Agarwal: The oscillation of an m-th order perturbed nonlinear difference equation. Arch. Math. (Brno) 32 (1996), 13-27.

    Google Scholar 

  17. A. Zafer: On the existence of positive solutions and the oscillation of solutions of higher order difference equations with forcing terms. Preprint.

  18. A. Zafer: Oscillatory and asymptotic behavior of higher order difference equations. Math. Comput. Modelling 21 (1995), 43-50.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Madras University P.G. Center, Salem-636, 011, Tamil Nadu, India

    E. Thandapani & R. Arul

Authors
  1. E. Thandapani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Arul
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Thandapani, E., Arul, R. Oscillatory and asymptotic behavior of solutions of higher order damped nonlinear difference equations. Czechoslovak Mathematical Journal 49, 149–161 (1999). https://doi.org/10.1023/A:1022420511275

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022420511275

Search

Navigation