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New Conditions for the Oscillation of Second-Order Differential Equations with Sublinear Neutral Terms

Author

Listed:
  • Shyam Sundar Santra

    (Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India
    These authors contributed equally to this work.)

  • Omar Bazighifan

    (Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen
    These authors contributed equally to this work.)

  • Mihai Postolache

    (Center for General Education, China Medical University, Taichung 40402, Taiwan
    Department of Interior Design, Asia University, Taichung 41354, Taiwan
    Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania
    Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania)

Abstract

In continuous applications in electrodynamics, neural networks, quantum mechanics, electromagnetism, and the field of time symmetric, fluid dynamics, neutral differential equations appear when modeling many problems and phenomena. Therefore, it is interesting to study the qualitative behavior of solutions of such equations. In this study, we obtained some new sufficient conditions for oscillations to the solutions of a second-order delay differential equations with sub-linear neutral terms. The results obtained improve and complement the relevant results in the literature. Finally, we show an example to validate the main results, and an open problem is included.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1159-:d:559071
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    References listed on IDEAS

    as
    1. Tongxing Li & Yuriy V. Rogovchenko, 2015. "Oscillation of second-order neutral differential equations," Mathematische Nachrichten, Wiley Blackwell, vol. 288(10), pages 1150-1162, July.
    2. 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.
    3. George E. Chatzarakis & Said R. Grace & Irena Jadlovská & Tongxing Li & Ercan Tunç, 2019. "Oscillation Criteria for Third-Order Emden–Fowler Differential Equations with Unbounded Neutral Coefficients," Complexity, Hindawi, vol. 2019, pages 1-7, August.
    4. Kuo‐Shou Chiu & Tongxing Li, 2019. "Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments," Mathematische Nachrichten, Wiley Blackwell, vol. 292(10), pages 2153-2164, October.
    5. 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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    Cited by:

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