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Journals / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 4

Oscillatory and asymptotic behavior of third-order nonlinear differential equations with a superlinear neutral term

Said R. GRACE
Irena JADLOVSKA
Ercan TUNÇ
Pages
1317–1329
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

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

Examples illustrating the resultsare included and some suggestions for further research are indicated.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Sufficient conditions are derived for all solutions of a class of third-order nonlinear differential equations witha superlinear neutral term to be either oscillatory or convergent to zero asymptotically.
📊
Key Findings & Data:Sufficient conditions are derived for all solutions of a class of third-order nonlinear differential equations witha superlinear neutral term to be either oscillatory or convergent to zero asymptotically.
💡
Conclusion & Impact:Examples illustrating the resultsare included and some suggestions for further research are indicated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Sufficient conditions are derived for all solutions of a class of third-order nonlinear differential equations witha superlinear neutral term to be either oscillatory or convergent to zero asymptotically. Examples illustrating the resultsare included and some suggestions for further research are indicated.

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Cite This Article

GRACE, S. R., JADLOVSKA, I., TUNÇ, E. (2022). Oscillatory and asymptotic behavior of third-order nonlinear differential equations with a superlinear neutral term. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 4, 1317–1329. https://ajindex.com/articles/608808

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References (5)

  1. Agarwal RP, Grace SR, O’Regan D. Oscillation theory for difference and functional differential equations. Dordrecht, Netherlands: Kluwer Academic Publishers, 2010
  2. Baculíková B, Džurina J. Oscillation of third-order neutral differential equations. Mathematical and Computer Modelling 2010; 52 (1-2): 215-226. doi:10.1016/j.mcm.2010.02.011 [3] Chatzarakis GE, Džurina J, Jadlovská I. Oscillatory properties of third-order neutral delay differential equations with noncanonical operators. Mathematics 2019; 7(12): 1-12. doi:10.3390/math7121 [4] Chatzarakis GE, Grace SR, I. Jadlovská, Li T, Tunç E. Oscillation criteria for third-order Emden–Fowler differential equations with unbounded neutral coefficients. Complexity 2019; 2019: 1-7. doi: 10.1155/2019/5691758 [5] Chen DX, Liu JC. Asymptotic behavior and oscilation of solutions of third-order nonlinear neutral delay dynamic equations on time scales. Canadian Applied Mathematcs Quarterly 2008; 16 (1): 19-43
  3. Das P. Oscillation criteria for odd order neutral equations. Journal of Mathematical Analysis and Applications 1994; 188 (1): 245-257. doi: 10.1006/jmaa.1994.1425 [7] Džurina J, Grace SR, Jadlovská I. On nonexistence of Kneser solutions of third-order neutral delay differential equations. Appllied Mathematics Letters 2019; 88: 193-200. doi: 10.1016/j.aml.2018.08.016 [8] Došlá Z, Liška P. Comparison theorems for third-order neutral differential equations. Electroninc Journal of Differential Equations 2016; 2016 (38): 1-13
  4. Grace SR, Graef JR, El-Beltagy MA. On the oscillation of third order neutral delay dynamic equations on time scales. Computers & Mathematics with Applications 2012; 63 (4): 775-782. doi: 10.1016/j.camwa.2011.11.042 [10] Grace SR, Graef JR, Tunç E. Oscillatory behaviour of third order nonlinear differential equations with a nonlinear nonpositive neutral term. Journal of Taibah University for Science 2019; 13 (1): 704-710. doi: 10.1080/16583655.2019.1622847 [11] Graef JR, Savithri R, Thandapani E. Oscillatory properties of third order neutral delay differential equations. In: Proceedings of the fourth international conference on dynamical systems and differential equations; Wilmington, NC, USA; 2002. pp. 342-350
  5. Graef JR, Tunç E, Grace SR. Oscillatory and asymptotic behavior of a third-order nonlinear neutral differential equation. Opuscula Mathematica 2017; 37 (6): 839-852. doi: 10.7494/OpMath.2017.37.6.839 [13] Graef JR, Spikes WP, Grammatikopoulos MK. Asymptotic behavior o