Skip to main content
SpringerLink
Log in

Asymptotic behavior of positive solutions of fourth-order nonlinear difference equations

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We consider a class of fourth-order nonlinear difference equations of the form {fx006-01} where α, β are ratios of odd positive integers and {p n}, {q n} are positive real sequences defined for all n ∈ ℕ(n 0). We establish necessary and sufficient conditions for the existence of nonoscillatory solutions with specific asymptotic behavior under suitable combinations of convergence or divergence conditions for the sums {fx006-02}.

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, M. Bohner, S. R. Grace, and D. O’Regan, Discrete Oscillation Theory, Hindawi, New York (2005).

    MATH  Google Scholar 

  2. R. P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York (1992).

    MATH  Google Scholar 

  3. R. P. Agarwal, S. R. Grace, and D. O’Regan, “On the oscillation of certain third-order difference equations,” Adv. Difference Equat., 2005, No. 3, 345–367 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  4. S. R. Grace and B. S. Lalli, “Oscillation of higher-order nonlinear difference equations,” Math. Comput. Model., 41, 485–491 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  5. W. T. Li and R. P. Agarwal, “Positive solutions of higher-order nonlinear delay difference equations,” Comput. Math. Appl., 45, 1203–1211 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  6. W. T. Li, S. S. Cheng, and G. Zhang, “A classification scheme for nonoscillatory solutions of a higher-order neutral nonlinear difference equation,” J. Austral. Math. Soc., Ser. A, 67, 122–142 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  7. B. Zhang and Y. J. Sun, “Classification of nonoscillatory solutions of a higher order neutral difference equation,” J. Difference Equat. Appl., 8, 937–955 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  8. Z. Zhu, G. Wang, and S. S. Cheng, “A classification scheme for nonoscillatory solutions of a higher order neutral difference equation,” Adv. Difference Equat., 2006, 1–19 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Migda and E. Schmeidel, “Asymptotic properties of fourth-order nonlinear difference equations,” Math. Comput. Model., 39, 1203–1211 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Migda, A. Musielak, and E. Schmeidel, “On a class of fourth-order nonlinear difference equations,” Adv. Difference Equat., 2004, No. 1, 23–36 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  11. B. Liu and J. Yan, “Oscillatory and asymptotic behavior of fourth-order nonlinear difference equations,” Acta Math. Sinica, 13, 105–115 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  12. E. Schmeidel, “Oscillation and nonoscillation theorems for fourth order difference equations,” Rocky Mountain J. Math., 33, 1083–1094 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  13. E. Thandapani and B. Selvaraj, “Oscillatory and nonoscillatory behavior of fourth order quasilinear difference equations,” Far East J. Appl. Math., 17, No. 3, 287–307 (2004).

    MATH  MathSciNet  Google Scholar 

  14. B. G. Zhang and S. S. Cheng, “On a class of nonlinear difference equations,” J. Difference Equat. Appl., 1, 391–411 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  15. R. P. Agarwal and J. V. Manojlović, “Asymptotic behavior of nonoscillatory solutions of fourth order nonlinear difference equations,” Dynam. Continuous, Discrete and Impulsive Systems (to appear).

Download references

Author information

Authors and Affiliations

  1. Florida Institute of Technology, Melbourne, USA

    R. P. Agarwal

  2. University of Niš, Niš, Serbia

    J. V. Manojlović

Authors
  1. R. P. Agarwal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. V. Manojlović
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 8–27, January, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Agarwal, R.P., Manojlović, J.V. Asymptotic behavior of positive solutions of fourth-order nonlinear difference equations. Ukr Math J 60, 6–28 (2008). https://doi.org/10.1007/s11253-008-0039-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-008-0039-2

Keywords

Search

Navigation