Opuscula Math. 39, no. 6 (2019), 753-763
https://doi.org/10.7494/OpMath.2019.39.6.753

 
Opuscula Mathematica

Oscillatory criteria for second order differential equations with several sublinear neutral terms

Blanka Baculikova

Abstract. In this paper, sufficient conditions for oscillation of the second order differential equations with several sublinear neutral terms are established. The results obtained generalize and extend those reported in the literature. Several examples are included to illustrate the importance and novelty of the presented results.

Keywords: second order neutral differential equation, sub-linear neutral term, oscillation.

Mathematics Subject Classification: 34K11, 34C10.

Full text (pdf)

  1. R.P. Agarwal, M. Bohner, W.T. Li, Nonoscillation and Oscillation: Theory of Functional Differential Equations, Marcel Dekker, New York, 2004.
  2. R.P. Agarwal, M. Bohner, T. Li, C. Zhang, Oscillation of second order differential equations with a sublinear neutral term, Carpathian J. Math. 30 (2014), 1-6.
  3. R.P. Agarwal, S.R. Grace, D. O'Regan, Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations, Kluwer, Dordrecht, 2002.
  4. B. Baculikova, J. Dzurina, Oscillation theorems for second order nonlinear neutral differential equations, Comput. Math. Appl. 61 (2011), 94-99.
  5. B. Baculikova, T. Li, J. Dzurina, Oscillation theorems for second order superlinear neutral differential equations, Math. Slovaca 63 (2013), 123-134.
  6. M. Bohner, S.R. Grace, I. Jadlovska, Oscillation criteria for second order neutral delay differential equation, Electron. J. Qual. Theory Differ. Equ. 62 (2017), 1-12.
  7. J. Dzurina, R. Kotorova, Zero points of the solutions of a differential equation, Acta Electrotechnica et Informatica 7 (2007), 26-29.
  8. L.H. Erbe, Q. Kong, B.G. Zhang, Oscillation Theory For Functional Differential Equations, Marcel Dekker, New York, 1995.
  9. S.R. Grace, B.S. Lalli, Oscillation of nonlinear second order neutral delay differential equations, Rad. Math. 3 (1987), 77-84.
  10. J.K. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977.
  11. G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities, Cambridge University Press, London, 1934.
  12. M. Hasanbulli, Yu.V. Rogovchenko, Oscillation criteria for second order nonlinear neutral differential equations, Appl. Math. Comput. 215 (2010), 4392-4399.
  13. I. Jadlovska, Application of Lambert W function in oscillation theory, Acta Electrotechnica et Informatica 14 (2014), 9-17.
  14. G.S. Ladde, V. Lakshmikanthan, B.G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, Dekker, New York, 1987.
  15. T. Li, Z. Han, C. Zhang, S. Sun, On the oscillation of second order Emden-Fowler neutral differential equations, J. Appl. Math. Computing 37 (2011), 601-610.
  16. T. Li, R.P. Agarwal, M. Bohner, Some oscillation results for second order neutral differential equations, J. Indian Math. Soc. 79 (2012), 97-106.
  17. T. Li, Yu.V. Rogovchenko, C. Zhang, Oscillation of second order neutral differential equations, Funkc. Ekvac. 56 (2013), 111-120.
  18. T. Li, M.T. Senel, C. Zhang, Oscillation of solutions to second order half-linear differential equations with neutral terms, Eletronic J. Differ. Equ. 2013 (2013) 229, 1-7.
  19. T. Li, E. Thandapani, J.R. Greaf, E. Tunc, Oscillation of second order Emden-Fowler neutral differential equations, Nonlinear Stud. 20 (2013), 1-8.
  20. S. Tamilvanan, E. Thandapani, J. Dzurina, Oscillation of second order nonlinear differential eqation with sublinear neutral term, Diff. Equ. Appl. 9 (2017), 29-35.
  21. S. Tamilvanan, E. Thandapani, S.R. Grace, Oscillation theorems for second-order non-linear differential equation with a non-linear neutral term, Int. J. Dyn. Syst. Differ. Equ. 7 (2017), 316-327.
  22. E. Thandapani, R. Rama, Comparison and oscillation theorems for second order nonlinear neutral differential equations, Serdica Math. J. 39 (2013), 1-16.
  23. R. Xu, F.W. Meng, Oscillation criteria for second order quasilinear neutral delay differential equations, Appl. Math. Comput. 192 (2007), 216-222.
  24. C. Zhang, M.T. Senel, T. Li, Oscillation of second order half-linear differential equations with several neutral terms, J. Appl. Math. Comput. 44 (2014), 511-518.
  • Blanka Baculikova
  • Department of Mathematics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00 Košice, Slovakia
  • Communicated by Josef Diblík.
  • Received: 2019-02-27.
  • Revised: 2019-09-09.
  • Accepted: 2019-09-10.
  • Published online: 2019-11-22.
Opuscula Mathematica - cover

Cite this article as:
Blanka Baculikova, Oscillatory criteria for second order differential equations with several sublinear neutral terms, Opuscula Math. 39, no. 6 (2019), 753-763, https://doi.org/10.7494/OpMath.2019.39.6.753

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.