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Nonlinear Differential Equations with Distributed Delay: Some New Oscillatory Solutions

Author

Listed:
  • Barakah Almarri

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

  • Ali Hasan Ali

    (Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq
    Doctoral School of Mathematical and Computational Sciences, University of Debrecen, H-4002 Debrecen, Hungary)

  • António M. Lopes

    (LAETA/INEGI, Faculty of Engineering, University of Porto, 4099-002 Porto, Portugal)

  • Omar Bazighifan

    (Department of Mathematics, Faculty of Science, Hadhramout University, Mukalla 50512, Yemen
    Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy)

Abstract

The oscillation of a class of fourth-order nonlinear damped delay differential equations with distributed deviating arguments is the subject of this research. We propose a new explanation of the fourth-order equation oscillation in terms of the oscillation of a similar well-studied second-order linear differential equation without damping. The extended Riccati transformation, integral averaging approach, and comparison principles are used to provide some additional oscillatory criteria. An example demonstrates the efficacy of the acquired criteria.

Suggested Citation

  • Barakah Almarri & Ali Hasan Ali & António M. Lopes & Omar Bazighifan, 2022. "Nonlinear Differential Equations with Distributed Delay: Some New Oscillatory Solutions," Mathematics, MDPI, vol. 10(6), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:995-:d:774927
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    References listed on IDEAS

    as
    1. M. Bartušek & M. Cecchi & Z. Došlá & M. Marini, 2012. "Fourth-Order Differential Equation with Deviating Argument," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-17, March.
    2. Chengmin Hou & Sui Sun Cheng, 2009. "Asymptotic Dichotomy in a Class of Fourth-Order Nonlinear Delay Differential Equations with Damping," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-7, June.
    3. Saad Althobati & Omar Bazighifan & Mehmet Yavuz, 2021. "Some Important Criteria for Oscillation of Non-Linear Differential Equations with Middle Term," Mathematics, MDPI, vol. 9(4), pages 1-9, February.
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    Citations

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    Cited by:

    1. 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.
    2. Uroosa Arshad & Mariam Sultana & Ali Hasan Ali & Omar Bazighifan & Areej A. Al-moneef & Kamsing Nonlaopon, 2022. "Numerical Solutions of Fractional-Order Electrical RLC Circuit Equations via Three Numerical Techniques," Mathematics, MDPI, vol. 10(17), pages 1-16, August.
    3. Nikola Popović & Kemal Eren & Ana Savić & Soley Ersoy, 2023. "Framed Curve Families Induced by Real and Complex Coupled Dispersionless-Type Equations," Mathematics, MDPI, vol. 11(16), pages 1-13, August.
    4. Sorin Mureşan & Loredana Florentina Iambor & Omar Bazighifan, 2022. "New Applications of Perov’s Fixed Point Theorem," Mathematics, MDPI, vol. 10(23), pages 1-9, December.
    5. Ramasamy Vimala & Ramasamy Kodeeswaran & Robert Cep & Majella Jenvi Ignatia Krishnasamy & Meenakshi Awasthi & Govindasamy Santhakumar, 2023. "Oscillation of Nonlinear Neutral Delay Difference Equations of Fourth Order," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    6. Mnaouer Kachout & Clemente Cesarano & Amir Abdel Menaem & Taher S. Hassan & Belal A. Glalah, 2023. "Oscillation Criteria for Qusilinear Even-Order Differential Equations," Mathematics, MDPI, vol. 11(12), pages 1-11, June.
    7. 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.

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