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Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Author

Listed:
  • Shyam Sundar Santra

    (Department of Mathematics, JIS College of Engineering, Kalyani 741235, India)

  • Rami Ahmad El-Nabulsi

    (Research Center for Quantum Technology, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Athens Institute for Education and Research, Mathematics and Physics Divisions, 8 Valaoritou Street, Kolonaki, 10671 Athens, Greece)

  • Khaled Mohamed Khedher

    (Department of Civil Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia
    Department of Civil Engineering, High Institute of Technological Studies, Mrezgua University Campus, Nabeul 8000, Tunisia)

Abstract

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

Suggested Citation

  • Shyam Sundar Santra & Rami Ahmad El-Nabulsi & Khaled Mohamed Khedher, 2021. "Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator," Mathematics, MDPI, vol. 9(12), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1323-:d:570994
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    References listed on IDEAS

    as
    1. Shyam Sundar Santra & Omar Bazighifan & Hijaz Ahmad & Shao-Wen Yao, 2020. "Second-Order Differential Equation with Multiple Delays: Oscillation Theorems and Applications," Complexity, Hindawi, vol. 2020, pages 1-6, November.
    2. Rihan, F.A. & Abdel Rahman, D.H. & Lakshmanan, S. & Alkhajeh, A.S., 2014. "A time delay model of tumour–immune system interactions: Global dynamics, parameter estimation, sensitivity analysis," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 606-623.
    3. Tongxing Li & Yuriy V. Rogovchenko, 2015. "Oscillation of second-order neutral differential equations," Mathematische Nachrichten, Wiley Blackwell, vol. 288(10), pages 1150-1162, July.
    4. Omar Bazighifan, 2020. "Some New Oscillation Results for Fourth-Order Neutral Differential Equations with a Canonical Operator," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-7, 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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