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An Improved Relationship between the Solution and Its Corresponding Function in Fourth-Order Neutral Differential Equations and Its Applications

Author

Listed:
  • Osama Moaaz

    (Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Clemente Cesarano

    (Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy)

  • Barakah Almarri

    (Department of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

Abstract

This work aims to derive new inequalities that improve the asymptotic and oscillatory properties of solutions to fourth-order neutral differential equations. The relationships between the solution and its corresponding function play an important role in the oscillation theory of neutral differential equations. Therefore, we improve these relationships based on the modified monotonic properties of positive solutions. Additionally, we set new conditions that confirm the absence of positive solutions and thus confirm the oscillation of all solutions of the considered equation. We finally explain the importance of the new inequalities by applying our results to some special cases of the studied equation, as well as comparing them with previous results in the literature.

Suggested Citation

  • Osama Moaaz & Clemente Cesarano & Barakah Almarri, 2023. "An Improved Relationship between the Solution and Its Corresponding Function in Fourth-Order Neutral Differential Equations and Its Applications," Mathematics, MDPI, vol. 11(7), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1708-:d:1114671
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    References listed on IDEAS

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    1. Taher S. Hassan & Yuangong Sun & Amir Abdel Menaem, 2020. "Improved Oscillation Results for Functional Nonlinear Dynamic Equations of Second Order," Mathematics, MDPI, vol. 8(11), pages 1-19, October.
    2. 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.
    3. Jehad Alzabut & Ravi P. Agarwal & Said R. Grace & Jagan M. Jonnalagadda & A. George Maria Selvam & Chao Wang, 2022. "A Survey on the Oscillation of Solutions for Fractional Difference Equations," Mathematics, MDPI, vol. 10(6), pages 1-28, March.
    4. 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.
    5. Taher S. Hassan & Said R. Grace, 2016. "Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-9, June.
    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.
    7. Osama Moaaz & Ali Muhib & Saud Owyed & Emad E. Mahmoud & Aml Abdelnaser & Kottakkaran Sooppy Nisar, 2021. "Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation," Journal of Mathematics, Hindawi, vol. 2021, pages 1-7, February.
    8. Barakah Almarri & Higinio Ramos & Osama Moaaz, 2022. "New Monotonic Properties of the Class of Positive Solutions of Even-Order Neutral Differential Equations," Mathematics, MDPI, vol. 10(9), pages 1-13, April.
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    Cited by:

    1. Osama Moaaz & Yousef Alnafisah, 2023. "An Improved Approach to Investigate the Oscillatory Properties of Third-Order Neutral Differential Equations," Mathematics, MDPI, vol. 11(10), pages 1-15, May.
    2. Mansour Alatwi & Osama Moaaz & Wedad Albalawi & Fahd Masood & Hamdy El-Metwally, 2024. "Asymptotic and Oscillatory Analysis of Fourth-Order Nonlinear Differential Equations with p -Laplacian-like Operators and Neutral Delay Arguments," Mathematics, MDPI, vol. 12(3), pages 1-23, February.
    3. Hail S. Alrashdi & Wedad Albalawi & Ali Muhib & Osama Moaaz & Elmetwally M. Elabbasy, 2024. "Kamenev-Type Criteria for Testing the Asymptotic Behavior of Solutions of Third-Order Quasi-Linear Neutral Differential Equations," Mathematics, MDPI, vol. 12(11), pages 1-16, June.

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