Skip to main content
SpringerLink
Log in

Oscillation criteria for second-order superlinear Emden–Fowler neutral differential equations

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

We study oscillatory behavior of solutions to a class of second-order superlinear Emden–Fowler neutral differential equations. New oscillation theorems are presented and their efficiency is illustrated.

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. Agarwal, R.P., Bohner, M., Li, T., Zhang, C.: Oscillation of second-order Emden–Fowler neutral delay differential equations. Ann. Mat. Pura Appl. (4) 193, 1861–1875 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Agarwal, R.P., Bohner, M., Li, W.-T.: Nonoscillation and Oscillation: Theory for Functional Differential Equations. Marcel Dekker Inc., New York (2004)

  3. Atkinson, F.V.: On second-order nonlinear oscillations. Pac. J. Math. 5, 643–647 (1955)

    Article  MATH  Google Scholar 

  4. Baculíková, B., Džurina, J.: Oscillation theorems for second-order nonlinear neutral differential equations. Comput. Math. Appl. 62, 4472–4478 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Baculíková, B., Li, T., Džurina, J.: Oscillation theorems for second-order superlinear neutral differential equations. Math. Slovaca 63, 123–134 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Berkovich, L.M.: The generalized Emden–Fowler equation. Sym. Nonlinear Math. Phys. 1, 155–163 (1997)

    MathSciNet  MATH  Google Scholar 

  7. Erbe, L., Kong, Q., Zhang, B.G.: Oscillation Theory for Functional Differential Equations. Marcel Dekker Inc., New York (1995)

  8. Győri, I., Ladas, G.: Oscillation Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford (1991)

    MATH  Google Scholar 

  9. Hale, J.K.: Theory of Functional Differential Equations. Springer, New York (1977)

    Book  MATH  Google Scholar 

  10. Kamenev, I.V.: An integral criterion for oscillation of linear differential equations of second-order. Mat. Zamet. 23, 249–251 (1978). (in Russian)

    MATH  Google Scholar 

  11. Li, T., Rogovchenko, Yu.V.: Asymptotic behavior of higher-order quasilinear neutral differential equations. Abstr. Appl. Anal. 2014, 1–11 (2014)

  12. Li, T., Rogovchenko, Yu.V., Zhang, C.: Oscillation of second-order neutral differential equations. Funkc. Ekvac. 56, 111–120 (2013)

  13. Philos, Ch.G.: Oscillation theorems for linear differential equations of second order. Arch. Math. 53, 482–492 (1989)

  14. Saker, S.H., Manojlović, J.V.: Oscillation criteria for second order superlinear neutral delay differential equations. Electron J. Qual. Theory Differ. Equ. 2004, 1–22 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wong, J.S.W.: On the generalized Emden–Fowler equation. SIAM Rev. 17, 339–360 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  16. Xu, Z.T.: On the oscillation of second order neutral differential equations of Emden–Fowler type. Monatsh. Math. 150, 157–171 (2007)

Download references

Acknowledgements

The research of the first author is supported by NNSF of P.R. China (Grant No. 61503171), CPSF (Grant No. 2015M582091), NSF of Shandong Province (Grant No. ZR2016JL021), DSRF of Linyi University (Grant No. LYDX2015BS001), and the AMEP of Linyi University, P.R. China.

Author information

Authors and Affiliations

  1. LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Linyi University, Linyi, 276005, Shandong, People’s Republic of China

    Tongxing Li

  2. School of Informatics, Linyi University, Linyi, 276005, Shandong, People’s Republic of China

    Tongxing Li

  3. Department of Mathematical Sciences, University of Agder, Post Box 422, 4604, Kristiansand, Norway

    Yuriy V. Rogovchenko

Authors
  1. Tongxing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuriy V. Rogovchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuriy V. Rogovchenko.

Additional information

Communicated by A. Constantin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, T., Rogovchenko, Y.V. Oscillation criteria for second-order superlinear Emden–Fowler neutral differential equations. Monatsh Math 184, 489–500 (2017). https://doi.org/10.1007/s00605-017-1039-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00605-017-1039-9

Keywords

Mathematics Subject Classification

Search

Navigation