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New oscillation criteria for nonlinear delay differential equations of fourth-order

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  • Moaaz, Osama
  • Muhib, Ali

Abstract

By using a generalized Riccati substitution, we present a new criterion for oscillation of solutions of fourth-order quasi-linear differential equations (r(t)(x‴(t))α)′ + f(t,x(σ(t)))=0, in noncanonical case ∫∞r−1/α(s)ds < ∞. We utilize an approach that gives rise to two or three independent conditions, eliminating non-oscillatory solutions. Moreover, we establish conditions in a non-traditional form (limsup(·)>1), while condition (limsup(·)=∞) cannot be applied. Our results essentially improve and complement a number of related ones. Examples are provided to illustrate the results.

Suggested Citation

  • Moaaz, Osama & Muhib, Ali, 2020. "New oscillation criteria for nonlinear delay differential equations of fourth-order," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    • Handle: RePEc:eee:apmaco:v:377:y:2020:i:c:s0096300320301612
    DOI: 10.1016/j.amc.2020.125192
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    References listed on IDEAS

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    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. 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.
    3. Chatzarakis, G.E. & Džurina, J. & Jadlovská, I., 2019. "New oscillation criteria for second-order half-linear advanced differential equations," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 404-416.
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    1. 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.
    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. Higinio Ramos & Osama Moaaz & Ali Muhib & Jan Awrejcewicz, 2021. "More Effective Results for Testing Oscillation of Non-Canonical Neutral Delay Differential Equations," Mathematics, MDPI, vol. 9(10), pages 1-10, May.
    4. Barakah Almarri & Osama Moaaz, 2023. "Improved Properties of Positive Solutions of Higher Order Differential Equations and Their Applications in Oscillation Theory," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    5. 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).
    6. Osama Moaaz & Clemente Cesarano, 2021. "New Asymptotic Properties of Positive Solutions of Delay Differential Equations and Their Application," Mathematics, MDPI, vol. 9(16), pages 1-9, August.
    7. Ioannis Dassios & Ali Muhib & Sobhy A. A. El-Marouf & Sayed K. Elagan, 2023. "Oscillation of Neutral Differential Equations with Damping Terms," Mathematics, MDPI, vol. 11(2), pages 1-15, January.
    8. 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.
    9. Omar Bazighifan & Thabet Abdeljawad, 2020. "Improved Approach for Studying Oscillatory Properties of Fourth-Order Advanced Differential Equations with p -Laplacian Like Operator," Mathematics, MDPI, vol. 8(5), pages 1-11, April.
    10. Osama Moaaz & Jan Awrejcewicz & Ali Muhib, 2020. "Establishing New Criteria for Oscillation of Odd-Order Nonlinear Differential Equations," Mathematics, MDPI, vol. 8(6), pages 1-15, June.
    11. Ghada AlNemer & Waed Muhsin & Osama Moaaz & Elmetwally M. Elabbasy, 2023. "On the Positive Decreasing Solutions of Half-Linear Delay Differential Equations of Even Order," Mathematics, MDPI, vol. 11(6), pages 1-12, March.
    12. Osama Moaaz & Dumitru Baleanu & Ali Muhib, 2020. "New Aspects for Non-Existence of Kneser Solutions of Neutral Differential Equations with Odd-Order," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    13. 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.
    14. Osama Moaaz & Belgees Qaraad & Rami Ahmad El-Nabulsi & Omar Bazighifan, 2020. "New Results for Kneser Solutions of Third-Order Nonlinear Neutral Differential Equations," Mathematics, MDPI, vol. 8(5), pages 1-12, May.
    15. 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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