IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i10p1111-d554641.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/10/1111/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/10/1111/
    Download Restriction: no
    ---><---

    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. Yingzhu Wu & Yuanhong Yu & Jinsen Xiao, 2022. "Oscillation of Second Order Nonlinear Neutral Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    4. 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.
    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. 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.
    7. Osama Moaaz & Rami Ahmad El-Nabulsi & Ali Muhib & Sayed K. Elagan & Mohammed Zakarya, 2021. "New Improved Results for Oscillation of Fourth-Order Neutral Differential Equations," Mathematics, MDPI, vol. 9(19), pages 1-12, September.
    8. 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.
    9. Irena Jadlovská, 2021. "New Criteria for Sharp Oscillation of Second-Order Neutral Delay Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-23, August.
    10. 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.
    11. Rongrong Guo & Qingdao Huang & Qingmin Liu, 2021. "Some New Oscillation Criteria of Even-Order Quasi-Linear Delay Differential Equations with Neutral Term," Mathematics, MDPI, vol. 9(17), pages 1-11, August.
    12. Bazighifan, Omar, 2020. "On the oscillation of certain fourth-order differential equations with p-Laplacian like operator," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    13. Zuhur Alqahtani & Belgees Qaraad & Areej Almuneef & Higinio Ramos, 2024. "Asymptotic and Oscillatory Analysis of Second-Order Differential Equations with Distributed Deviating Arguments," Mathematics, MDPI, vol. 12(22), pages 1-19, November.
    14. Chatzarakis, G.E. & Džurina, J. & Jadlovská, I., 2019. "New oscillation criteria for second-order half-linear advanced differential equations," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 404-416.
    15. Omar Bazighifan & Ioannis Dassios, 2020. "Riccati Technique and Asymptotic Behavior of Fourth-Order Advanced Differential Equations," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    16. Chiu, Kuo-Shou & Li, Tongxing, 2022. "New stability results for bidirectional associative memory neural networks model involving generalized piecewise constant delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 719-743.
    17. K. S. Vidhyaa & John R. Graef & E. Thandapani, 2020. "New Oscillation Results for Third-Order Half-Linear Neutral Differential Equations," Mathematics, MDPI, vol. 8(3), pages 1-9, March.
    18. Omar Bazighifan & Clemente Cesarano, 2019. "Some New Oscillation Criteria for Second Order Neutral Differential Equations with Delayed Arguments," Mathematics, MDPI, vol. 7(7), pages 1-9, July.
    19. Marappan Sathish Kumar & Omar Bazighifan & Alanoud Almutairi & Dimplekumar N. Chalishajar, 2021. "Philos-Type Oscillation Results for Third-Order Differential Equation with Mixed Neutral Terms," Mathematics, MDPI, vol. 9(9), pages 1-9, April.
    20. Moaaz, Osama & Muhib, Ali, 2020. "New oscillation criteria for nonlinear delay differential equations of fourth-order," Applied Mathematics and Computation, Elsevier, vol. 377(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1111-:d:554641. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.