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

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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 δ u ‴ α ′ + q u x β ϕ 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
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    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.
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    Cited by:

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