IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i19p2388-d643157.html
   My bibliography  Save this article

New Improved Results for Oscillation of Fourth-Order Neutral Differential Equations

Author

Listed:
  • Osama Moaaz

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy)

  • 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)

  • Ali Muhib

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Department of Mathematics, Faculty of Education—Al-Nadirah, Ibb University, Ibb 999101, Yemen)

  • Sayed K. Elagan

    (Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
    Department of Mathematics and Computer Sciences, Faculty of Science, Menoufia University, Shebin Elkom 32511, Egypt)

  • Mohammed Zakarya

    (Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
    Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt)

Abstract

In this study, a new oscillation criterion for the fourth-order neutral delay differential equation r u x u + p u x ? u ? ? ? + q u x ? ? u = 0 , u ? u 0 is established. By introducing a Riccati substitution, we obtain a new criterion for oscillation without requiring the existence of the unknown function. Furthermore, the new criterion improves and complements the previous results in the literature. The results obtained are illustrated by an example.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2388-:d:643157
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/19/2388/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/19/2388/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Osama Moaaz & Dimplekumar Chalishajar & Omar Bazighifan, 2019. "Some Qualitative Behavior of Solutions of General Class of Difference Equations," Mathematics, MDPI, vol. 7(7), pages 1-12, 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ali Muhib & Osama Moaaz & Clemente Cesarano & Shami A. M. Alsallami & Sayed Abdel-Khalek & Abd Elmotaleb A. M. A. Elamin, 2022. "New Monotonic Properties of Positive Solutions of Higher-Order Delay Differential Equations and Their Applications," Mathematics, MDPI, vol. 10(10), pages 1-12, May.

    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. Osama Moaaz & Fahd Masood & Clemente Cesarano & Shami A. M. Alsallami & E. M. Khalil & Mohamed L. Bouazizi, 2022. "Neutral Differential Equations of Second-Order: Iterative Monotonic Properties," Mathematics, MDPI, vol. 10(9), pages 1-11, April.
    2. 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.
    3. 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.
    4. 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).
    5. Asma Al-Jaser & Belgees Qaraad & Omar Bazighifan & Loredana Florentina Iambor, 2023. "Second-Order Neutral Differential Equations with Distributed Deviating Arguments: Oscillatory Behavior," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    6. Maryam Al-Kandari, 2023. "Conditions for the Oscillation of Solutions to Neutral Differential Equations of Higher Order," Mathematics, MDPI, vol. 11(24), pages 1-9, December.
    7. Mohamed Mazen & Mohamed M. A. El-Sheikh & Samah Euat Tallah & Gamal A. F. Ismail, 2025. "On the Oscillation of Fourth-Order Delay Differential Equations via Riccati Transformation," Mathematics, MDPI, vol. 13(3), pages 1-12, January.
    8. 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.
    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. Osama Moaaz & Ioannis Dassios & Omar Bazighifan & Ali Muhib, 2020. "Oscillation Theorems for Nonlinear Differential Equations of Fourth-Order," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    11. Awatif A. Hindi & Osama Moaaz & Clemente Cesarano & Wedad R. Alharbi & Mohamed A. Abdou, 2021. "Noncanonical Neutral DDEs of Second-Order: New Sufficient Conditions for Oscillation," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    12. 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.
    13. Osama Moaaz & Clemente Cesarano, 2021. "New Asymptotic Properties of Positive Solutions of Delay Differential Equations and Their Application," Mathematics, MDPI, vol. 9(16), pages 1-9, August.
    14. Jozef Dzurina, 2024. "Oscillation of Bounded Solutions of Delay Differential Equations," Mathematics, MDPI, vol. 13(1), pages 1-8, December.
    15. Omar Bazighifan & Mihai Postolache, 2020. "Improved Conditions for Oscillation of Functional Nonlinear Differential Equations," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    16. Alanoud Almutairi & Ali Hasan Ali & Omar Bazighifan & Loredana Florentina Iambor, 2023. "Oscillatory Properties of Fourth-Order Advanced Differential Equations," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    17. Yingzhu Wu & Yuanhong Yu & Jinsen Xiao, 2022. "Oscillation of Second Order Nonlinear Neutral Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    18. 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.
    19. 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.
    20. 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.

    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:19:p:2388-:d:643157. 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.