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Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term

Author

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  • Jozef Džurina
  • Said R. Grace
  • Irena Jadlovská
  • Tongxing Li

Abstract

New oscillation criteria for the second‐order Emden–Fowler delay differential equation with a sublinear neutral term are presented. An essential feature of our results is that oscillation of the studied equation is ensured via only one condition. Furthermore, as opposed to the results by Agarwal et al. (Ann. Mat. Pura Appl. (4) 193 (2014), no. 6, 1861–1875), Li and Rogovchenko (Math. Nachr. 288 (2015), no. 10, 1150–1162; Monatsh. Math. 184 (2017), no. 3, 489–500), and Xu (Monatsh. Math. 150 (2007), no. 2, 157–171), new criteria can be applied to Emden–Fowler delay differential equations with noncanonical operators and a sublinear neutral term. Our results essentially improve, extend, and simplify some known ones reported in the literature. The results are illustrated with examples.

Suggested Citation

  • Jozef Džurina & Said R. Grace & Irena Jadlovská & Tongxing Li, 2020. "Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term," Mathematische Nachrichten, Wiley Blackwell, vol. 293(5), pages 910-922, May.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:5:p:910-922
    DOI: 10.1002/mana.201800196
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    References listed on IDEAS

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    1. Tongxing Li & Yuriy V. Rogovchenko, 2014. "Asymptotic Behavior of Higher-Order Quasilinear Neutral Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, January.
    2. Tongxing Li & Yuriy V. Rogovchenko, 2015. "Oscillation of second-order neutral differential equations," Mathematische Nachrichten, Wiley Blackwell, vol. 288(10), pages 1150-1162, July.
    3. Agarwal, Ravi P. & Zhang, Chenghui & Li, Tongxing, 2016. "Some remarks on oscillation of second order neutral differential equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 178-181.
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    1. Ağacık Zafer & Tuncay Candan & Zeynep Nilhan Gürkan, 2025. "Equivalence Transformation for Neutral Differential Equations: Oscillation of Solutions," Mathematics, MDPI, vol. 13(14), pages 1-11, July.
    2. Haifeng Tian & Rongrong Guo, 2024. "Some Oscillatory Criteria for Second-Order Emden–Fowler Neutral Delay Differential Equations," Mathematics, MDPI, vol. 12(10), pages 1-15, May.
    3. Yang-Cong Qiu & Kuo-Shou Chiu & Said R. Grace & Qingmin Liu & Irena Jadlovská, 2021. "Oscillation of Solutions to Third-Order Nonlinear Neutral Dynamic Equations on Time Scales," Mathematics, MDPI, vol. 10(1), pages 1-12, December.
    4. Yingzhu Wu & Yuanhong Yu & Jinsen Xiao, 2022. "Oscillation of Second Order Nonlinear Neutral Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    5. A. A. El-Gaber & M. M. A. El-Sheikh & Haytham M. Rezk & Mohammed Zakarya & Ghada AlNemer & E. I. El-Saedy, 2024. "On the Oscillatory Behavior of Solutions of Second-Order Damped Differential Equations with Several Sub-Linear Neutral Terms," Mathematics, MDPI, vol. 12(20), pages 1-16, October.
    6. Shyam Sundar Santra & Abhay Kumar Sethi & Osama Moaaz & Khaled Mohamed Khedher & Shao-Wen Yao, 2021. "New Oscillation Theorems for Second-Order Differential Equations with Canonical and Non-Canonical Operator via Riccati Transformation," Mathematics, MDPI, vol. 9(10), pages 1-11, May.
    7. Fátima Cruz & Ricardo Almeida & Natália Martins, 2021. "Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels," Mathematics, MDPI, vol. 9(14), pages 1-18, July.
    8. Grace, Said R. & Negi, Shekhar Singh & Abbas, Syed, 2022. "New oscillatory results for non-linear delay dynamic equations with super-linear neutral term," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    9. Osama Moaaz & Ali Muhib & Shyam S. Santra, 2021. "An Oscillation Test for Solutions of Second-Order Neutral Differential Equations of Mixed Type," Mathematics, MDPI, vol. 9(14), pages 1-14, July.
    10. Shyam Sundar Santra & Omar Bazighifan & Mihai Postolache, 2021. "New Conditions for the Oscillation of Second-Order Differential Equations with Sublinear Neutral Terms," Mathematics, MDPI, vol. 9(11), pages 1-9, May.

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