Skip to main content
SpringerLink
Log in

Oscillation of Second Order Nonlinear Mixed Neutral Differential Equations with Distributed Deviating Arguments

  • Published:
Bulletin of the Malaysian Mathematical Sciences Society Aims and scope Submit manuscript

Abstract

In this work, some new oscillation criteria are established for a second-order nonlinear mixed neutral differential equation with distributed deviating arguments. Several examples are also provided to illustrate these 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. Agarwal, R.P., Grace, S.R., O’Regan, D.: Oscillation Theory of Differential and Functional Differential Equations. Kluwer, Dordrecht (2000)

    Book  Google Scholar 

  2. Baculíková, B.: Oscillation criteria for second order nonlinear differential equations. Arch. Math. 42, 141–149 (2006)

    MATH  Google Scholar 

  3. Baculíková, B., Džurina, J.: Oscillation of third-order neutral differential equations. Math. Comput. Model. 52, 215–226 (2010)

    Article  MATH  Google Scholar 

  4. Baculíková, B., Džurina, J., Li, T.: Oscillation results for even-order quasilinear neutral functional differential equations. Electron. J. Differ. Equ. 143, 1–9 (2011)

    Google Scholar 

  5. Candan, T.: Oscillation of solutions for odd-order neutral functional differential equations. Electron. J. Differ. Equ. 2010, 1–10 (2010)

    MathSciNet  Google Scholar 

  6. Candan, T.: Oscillation behavior of solutions for even order neutral functional differential equations. Appl. Math. Mech. Engl. 27, 1311–1320 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Candan, T., Dahiya, R.S.: On the oscillation of certain mixed neutral equations. Appl. Math. Lett. 21, 222–226 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Candan, T., Dahiya, R.S.: Oscillation of mixed neutral functional differential equations with distributed deviating arguments. Differ. Equ. Dyn. Syst. 16, 207–223 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dong, J.G.: Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments. Comput. Math. Appl. 59, 3710–3717 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  10. Džurina, J.: Oscillation of second-order differential equations with mixed argument. J. Math. Anal. Appl. 190, 821–828 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  11. Džurina, J.: Oscillation theorems for second order advanced neutral differential equations. Tatra Mt. Math. Publ. 48, 61–79 (2011)

    MATH  MathSciNet  Google Scholar 

  12. Džurina, J., Busa, J., Airyan, E.A.: Oscillation criteria for second-order differential equations of neutral type with mixed arguments. Differ. Equ. 38, 137–140 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Džurina, J., Hudáková, D.: Oscillation of second order neutral delay differential equations. Math. Bohem. 134, 31–38 (2009)

    MATH  MathSciNet  Google Scholar 

  14. Džurina, J., Stavroulakis, I.P.: Oscillation criteria for second-order delay differential equations. Appl. Math. Comput. 140, 445–453 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Erbe, L., Kong, Q.: Oscillation results for second order neutral differential equations. Funkc. Ekvacioj 35, 545–557 (1992)

    MATH  MathSciNet  Google Scholar 

  16. Grace, S.R.: On the oscillations of mixed neutral equations. J. Math. Anal. Appl. 194, 377–388 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  17. Grace, S.R., Lalli, B.S.: Oscillation of nonlinear second order neutral delay differential equations. Rad. Mat. 3, 77–84 (1987)

    MATH  MathSciNet  Google Scholar 

  18. Grammatikopoulos, M.K., Ladas, G., Meimaridou, A.: Oscillation of second order neutral delay differential equations. Rad. Mat. 1, 267–274 (1985)

    MATH  MathSciNet  Google Scholar 

  19. Hale, J.K.: Theory of Functional Differential Equations. Spring-Verlag, New York (1977)

    Book  MATH  Google Scholar 

  20. Han, Z., Li, T., Sun, S., Sun, Y.: Remarks on the paper [Appl. Math. Comput. 207 (2009) 388–396]. Appl. Math. Comput. 215(2010), 3998–4007 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  21. Han, Z., Li, T., Zhang, C., Sun, S.: Oscillatory behavior of solutions of certain third-order mixed neutral functional differential equations. Bull. Malays. Math. Sci. Soc. 35, 611–620 (2012)

    MATH  MathSciNet  Google Scholar 

  22. Hasanbulli, M., Rogovchenko, YuV: Oscillation criteria for second order nonlinear neutral differential equations. Appl. Math. Comput. 215, 4392–4399 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  23. Li, T.: Comparison theorems for second-order neutral differential equations of mixed type. Electron. J. Differ. Equ. 167, 1–7 (2010)

    Google Scholar 

  24. Li, T., Baculíková, B., Džurina, J.: Oscillation results for second-order neutral differential equations of mixed type. Tatra Mt. Math. Publ. 48, 101–116 (2011)

    MATH  MathSciNet  Google Scholar 

  25. Li, T., Han, Z., Sun, S., Zhao, Y.: Oscillation results for third order nonlinear delay dynamic equations on time scales. Bull. Malays. Math. Sci. Soc. 31, 639–648 (2011)

    MathSciNet  Google Scholar 

  26. Liu, L.H., Bai, Y.Z.: New oscillation criteria for second-order nonlinear neutral delay differential equations. J. Comput. Appl. Math. 231, 657–663 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  27. Philos, ChG: Oscillation theorems for linear differential equations of second order. Arch. Math. (Basel) 53, 482–492 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  28. Saker, S.H.: Oscillation of second order neutral delay differential equations of Emden-Fowler type. Acta Math. Hung. 100, 37–62 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  29. Sun, S., Li, T., Han, Z., Zhang, C.: On oscillation of second-order nonlinear neutral functional differential equations, Bull. Malays. Math. Sci. Soc. (2012) (in press)

  30. Tang, S., Gao, C., Li, T.: Oscillation theorems for second-order quasi-linear delay dynamic equations, Bull. Malays. Math. Sci. Soc. (2012) (in press)

  31. Thandapani, E., Piramanantham, V.: Oscillation criteria of second order neutral delay dynamic equations with distributed deviating arguments. Electron. J. Qual. Theory Differ. Equ. 61, 1–15 (2010)

    MathSciNet  Google Scholar 

  32. Wang, P.G.: Oscillation criteria for second order neutral equations with distributed deviating arguments. Comput. Math. Appl. 47, 1935–1946 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  33. Wang, P.G.: Oscillation properties for even order neutral equations with distributed deviating arguments. J. Comput. Appl. Math. 182, 290–303 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  34. Xu, R., Meng, F.W.: Oscillation criteria for second order quasi-linear neutral delay differential equations. Appl. Math. Comput. 192, 216–222 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  35. Xu, Z.T., Weng, P.X.: Oscillation of second-order neutral equations with distributed deviating arguments. J. Comput. Appl. Math. 202, 460–477 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  36. Yan, J.R.: Oscillation of higher order neutral differential equations. J. Aust. Math. Soc. (Series A) 64, 73–81 (1998)

    Article  MATH  Google Scholar 

  37. Yu, Y.H., Fu, X.L.: Oscillation of second order neutral equation with continuous distributed deviating argument. Rad. Mat. 7, 167–176 (1991)

    MATH  MathSciNet  Google Scholar 

  38. Zhao, J.H., Meng, F.W.: Oscillation criteria for second-order neutral equations with distributed deviating argument. Appl. Math. Comput. 206, 485–493 (2008)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors sincerely thank the Editors and reviewers for their valuable suggestions and useful comments that have led to the present improved version of the original manuscript.

Author information

Authors and Affiliations

  1. School of Science, Qingdao Technological University, Qingdao, Shandong, 266033, People’s Republic of China

    Yunsong Qi & Jinwei Yu

Authors
  1. Yunsong Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jinwei Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yunsong Qi.

Additional information

Norhashidah M. Ali.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qi, Y., Yu, J. Oscillation of Second Order Nonlinear Mixed Neutral Differential Equations with Distributed Deviating Arguments. Bull. Malays. Math. Sci. Soc. 38, 543–560 (2015). https://doi.org/10.1007/s40840-014-0035-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40840-014-0035-7

Keywords

Mathematics Subject Classification

Search

Navigation