IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i14p1634-d592167.html
   My bibliography  Save this article

An Oscillation Test for Solutions of Second-Order Neutral Differential Equations of Mixed Type

Author

Listed:
  • Osama Moaaz

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

  • Ali Muhib

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Department of Mathematics, Faculty of Education—Al-Nadirah, Ibb University, Ibb 70270, Yemen)

  • Shyam S. Santra

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

Abstract

It is easy to notice the great recent development in the oscillation theory of neutral differential equations. The primary aim of this work is to extend this development to neutral differential equations of mixed type (including both delay and advanced terms). In this work, we consider the second-order non-canonical neutral differential equations of mixed type and establish a new single-condition criterion for the oscillation of all solutions. By using a different approach and many techniques, we obtain improved oscillation criteria that are easy to apply on different models of equations.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1634-:d:592167
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/14/1634/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/14/1634/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Siyu Zhang & Fanwei Meng, 2010. "Oscillation Criteria for Even Order Neutral Equations with Distributed Deviating Argument," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-14, January.
    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. 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.
    2. Moaaz, Osama & Muhib, Ali, 2020. "New oscillation criteria for nonlinear delay differential equations of fourth-order," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Yingzhu Wu & Yuanhong Yu & Jinsen Xiao, 2022. "Oscillation of Second Order Nonlinear Neutral Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    8. Osama Moaaz & Mona Anis & Dumitru Baleanu & Ali Muhib, 2020. "More Effective Criteria for Oscillation of Second-Order Differential Equations with Neutral Arguments," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    9. 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.
    10. Zuzana Pátíková & Simona Fišnarová, 2021. "Use of the Modified Riccati Technique for Neutral Half-Linear Differential Equations," Mathematics, MDPI, vol. 9(3), pages 1-13, January.
    11. 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.
    12. 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.
    13. Devi, Munesh & Yadav, Shalini & Arora, Rajan, 2021. "Optimal system, invariance analysis of fourth-Order nonlinear ablowitz-Kaup-Newell-Segur water wave dynamical equation using lie symmetry approach," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Higinio Ramos & Osama Moaaz & Ali Muhib & Jan Awrejcewicz, 2021. "More Effective Results for Testing Oscillation of Non-Canonical Neutral Delay Differential Equations," Mathematics, MDPI, vol. 9(10), pages 1-10, May.
    19. Fátima Cruz & Ricardo Almeida & Natália Martins, 2021. "Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels," Mathematics, MDPI, vol. 9(14), pages 1-18, July.
    20. Amany Nabih & Osama Moaaz & Sameh S. Askar & Ahmad M. Alshamrani & Elmetwally M. Elabbasy, 2023. "Fourth-Order Neutral Differential Equation: A Modified Approach to Optimizing Monotonic Properties," Mathematics, MDPI, vol. 11(20), pages 1-15, October.

    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:14:p:1634-:d:592167. 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.