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Neutral Differential Equations of Second-Order: Iterative Monotonic Properties

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)

  • Fahd Masood

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Department of Mathematics, Faculty of Science, Sana’a University, Sana’a 12544, Yemen
    Department of Mathematics, Faculty of Education and Science, University of Sheba Region, Sheba Region 16822, Yemen)

  • Clemente Cesarano

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

  • Shami A. M. Alsallami

    (Department of Mathematical Sciences, College of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia)

  • E. M. Khalil

    (Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Mohamed L. Bouazizi

    (Department of Mechanical Engineering, College of Engineering, Prince Sattam bin Abdulaziz University, Alkharj 16273, Saudi Arabia)

Abstract

In this work, we investigate the oscillatory properties of the neutral differential equation ( r ( l ) [ ( s ( l ) + p ( l ) s ( g ( l ) ) ) ′ ] v ) ′ + ∑ i = 1 n q i ( l ) s v ( h i ( l ) ) = 0 , where s ≥ s 0 . We first present new monotonic properties for the solutions of this equation, and these properties are characterized by an iterative nature. Using these new properties, we obtain new oscillation conditions that guarantee that all solutions are oscillate. Our results are a complement and extension to the relevant results in the literature. We test the significance of the results by applying them to special cases of the studied equation.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1356-:d:796840
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    References listed on IDEAS

    as
    1. 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.
    2. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. 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.
    4. Moaaz, Osama & Muhib, Ali, 2020. "New oscillation criteria for nonlinear delay differential equations of fourth-order," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    5. 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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