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New Oscillation Theorems for Second-Order Differential Equations with Canonical and Non-Canonical Operator via Riccati Transformation

Author

Listed:
  • Shyam Sundar Santra

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

  • Abhay Kumar Sethi

    (Department of Mathematics, Sambalpur University, Sambalpur 768019, India)

  • Osama Moaaz

    (Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt)

  • 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)

  • Shao-Wen Yao

    (School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China)

Abstract

In this work, we prove some new oscillation theorems for second-order neutral delay differential equations of the form ( a ( ξ ) ( ( v ( ξ ) + b ( ξ ) v ( ϑ ( ξ ) ) ) ′ ) ) ′ + c ( ξ ) G 1 ( v ( κ ( ξ ) ) ) + d ( ξ ) G 2 ( v ( ς ( ξ ) ) ) = 0 under canonical and non-canonical operators, that is, ∫ ξ 0 ∞ d ξ a ( ξ ) = ∞ and ∫ ξ 0 ∞ d ξ a ( ξ ) < ∞ . We use the Riccati transformation to prove our main results. Furthermore, some examples are provided to show the effectiveness and feasibility of the main results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1111-:d:554641
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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. Omar Bazighifan & Marianna Ruggieri & Andrea Scapellato, 2020. "An Improved Criterion for the Oscillation of Fourth-Order Differential Equations," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

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