Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 2

Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term

İrena Jadlovska(Technical University of Košice)0000-0003-4649-5611
Zafer Ağacık(American University of the Middle East)0000-0001-8446-1223
Pages
—
Publication Date
2020-04-02
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The obtained results improve and correlate many of the known oscillation criteria in the literature for neutral and non-neutral equations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We study the oscillation problem for solutions of a class of $n$-th order nonlinear delay differential equations with nonpositive neutral terms.
📊
Key Findings & Data:We study the oscillation problem for solutions of a class of $n$-th order nonlinear delay differential equations with nonpositive neutral terms.
💡
Conclusion & Impact:The obtained results improve and correlate many of the known oscillation criteria in the literature for neutral and non-neutral equations.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Oscillation · neutral term · second order differential equation

Abstract

We study the oscillation problem for solutions of a class of $n$-th order nonlinear delay differential equations with nonpositive neutral terms. The obtained results improve and correlate many of the known oscillation criteria in the literature for neutral and non-neutral equations.

🔖

Cite This Article

Grace, S. R., Jadlovska, İ., Ağacık, Z. (2020). Oscillatory behavior of $n$-th order nonlinear delay differential equations with a nonpositive neutral term. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 2. https://doi.org/10.15672/hujms.471023

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (22)

  1. R.P. Agarwal, S.R. Grace, and D. O’Regan, Oscillation theory for second order linear, half-linear, superlinear and sublinear dynamic equations, Springer Science & Business Media, 2002.
  2. R.P. Agarwal, S.R. Grace, and P.J.Y. Wong, Oscillation theorems for certain higher order nonlinear functional differential equations, Appl. Anal. Discr. Math. 2, 1–30, 2008.
  3. R.P. Agarwal, M. Bohner, T. Li, and C. Zhang, A new approach in the study of oscillatory behavior of even-order neutral delay differential equations, Appl. Math. Comput. 225, 787–794, 2013.
  4. R.P. Agarwal, M. Bohner, T. Li, and C. Zhang, Oscillation of second order differential equations with a sublinear neutral term, Carpathian J. Math. 30 (1), 1–6, 2014.
  5. J.G. Dong, Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments, Comput. Math. Appl. 59, 3710 – 3717, 2010.
  6. S.R. Grace and B.S. Lalli, Oscillation of nonlinear second order neutral differential equations, Rat. Math. 3, 77 – 84, 1987.
  7. S.R. Grace, J.R. Graef, and M.A. El-Beltagy, On the oscillation of third order neutral delay dynamic equations on time scales, Comput. Math. Appl. 63 (4), 775–782, 2012.
  8. S.R. Grace and I. Jadlovská, Oscillation Criteria for second-order neutral damped differential equations with delay argument, in: Dynamical Systems - Analytical and Computational Techniques, InTech, 2017.
  9. S.R. Grace,Oscillatory behavior of second-order nonlinear differential equations with a nonpositive neutral term, Mediterr. J. Math. 14 (6), Art. 229, 2017.
  10. G.H. Hardy, I.E. Littlewood, and G. Polya, Inequalities, University Press, Cambridge, 1959.
  11. B. Karpuz, O. Ocalan, and S. Ozturk, Comparison theorems on the oscillation and asymptotic behaviour of higher-order neutral differential equations, Glasgow Math. J. 52 (1), 107–114, 2010.
  12. I.T. Kiguradze, On the oscillation of solutions of the Eq. $d^mu/dt^m+a(t)|u|^n {\rm sgn}u = 0$, Mat. Sb. 65, 172–187, 1964 (in Russian).
  13. T. Li, Z. Han, C. Zhang, and H. Li, Oscillation criteria for second-order superlinear neutral differential equations, Abstr. Appl. Anal. 2011, 2011.
  14. T. Li, Yu.V. Rogovchenko, and C. Zhang, Oscillation results for second-order nonlinear neutral differential equations, Adv. Differ. Equ. 2013, 1 – 13, 2013.
  15. Q. Li, R. Wang, F. Chen, and T. Li, Oscillation of second-order nonlinear delay differential equations with nonpositive neutral coefficients, Adv. Differ. Equ. 2015, 1–15, 2015.
  16. Ch. G. Philos, A new criterion for the oscillatory and asymptotic behavior of delay differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Mat. 39 (1), 61–64, 1981.
  17. H. Qin, N. Shang, and Y. Lu, A note on oscillation criteria of second order nonlinear neutral delay differential equations, Comput. Math. Appl. 56, 2987–299, 2008.
  18. V. Staikos and I. Stavroulakis, Bounded oscillations under the effect of retardations for differential equations of arbitrary order, P. Roy. Soc. Edinb. 77 (1), 129–136, 1977.
  19. H. Wu, L. Erbe, and A. Peterson, Oscillation of solution to second-order half-linear delay dynamic equations on time scales, Electron. J. Differ. Eq. 2016 (71), 1–15, 2016.
  20. J.S.W. Wong, Necessary and sufficient conditions for oscillation of second order neutral differential equations, J. Math. Anal. Appl. 252, 342–352, 2000.
  21. Q. Yang, l. Yang, and S. Zhu, Interval criteria for oscillation of second-order nonlinear neutral differential equations, Comput. Math. Appl. 46 (5), 903–918, 2003.
  22. Q. Li, R. Wang, F. Chen, and T. Li, Oscillation of second-order nonlinear delay differential equations with nonpositive neutral coefficients, Adv. Differ. Equ. 2015, 1–15, 2015.