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On the oscillation of certain fourth-order differential equations with p-Laplacian like operator

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  • Bazighifan, Omar

Abstract

The aim of this work is to study the oscillatory properties of the solutions of fourth-order delay differential equations with a p-Laplacian like operator of the form(r(ν)|w″′(ν)|p1−2w″′(ν))′+q(ν)|w(η(ν))|p2−2w(η(ν))=0.The results obtained are based on the comparison with first and second-order differential equations and the use of a Riccati transformation. Some examples are provided to illustrate the main results.

Suggested Citation

  • Bazighifan, Omar, 2020. "On the oscillation of certain fourth-order differential equations with p-Laplacian like operator," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304343
    DOI: 10.1016/j.amc.2020.125475
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Moaaz, Osama & Muhib, Ali, 2020. "New oscillation criteria for nonlinear delay differential equations of fourth-order," Applied Mathematics and Computation, Elsevier, vol. 377(C).
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    Cited by:

    1. 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).
    2. Lee, Dongsun & Lee, Chaeyoung, 2022. "Numerical solutions of the Allen–Cahn equation with the p-Laplacian," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    3. Omar Bazighifan & F. Ghanim & Jan Awrejcewicz & Khalil S. Al-Ghafri & Maryam Al-Kandari, 2021. "New Criteria for Oscillation of Half-Linear Differential Equations with p -Laplacian-like Operators," Mathematics, MDPI, vol. 9(20), pages 1-10, October.
    4. Khaled A. Gepreel, 2020. "Analytical Methods for Nonlinear Evolution Equations in Mathematical Physics," Mathematics, MDPI, vol. 8(12), pages 1-14, December.
    5. 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.

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