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New oscillation criteria for second-order half-linear advanced differential equations

Author

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  • Chatzarakis, G.E.
  • Džurina, J.
  • Jadlovská, I.

Abstract

The objective of this paper is to offer sufficient conditions for the oscillation and asymptotic behavior of all solutions of second-order half-linear differential equations with advanced argument of the form(r(y′)α)′(t)+q(t)yα(σ(t))=0,when ∫∞r−1/α(s)ds<∞. Our criteria substantially improve, simplify and complement a number of existing ones. The results obtained are illustrated by an example on the Euler type equations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:404-416
    DOI: 10.1016/j.amc.2018.10.091
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    References listed on IDEAS

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    1. Agarwal, Ravi P. & Bohner, Martin & Li, Tongxing & Zhang, Chenghui, 2015. "Even-order half-linear advanced differential equations: improved criteria in oscillatory and asymptotic properties," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 481-490.
    2. Tongxing Li & Yuriy V. Rogovchenko, 2015. "Oscillation of second-order neutral differential equations," Mathematische Nachrichten, Wiley Blackwell, vol. 288(10), pages 1150-1162, 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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    2. 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.
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    5. Taher S. Hassan & Qingkai Kong & Bassant M. El-Matary, 2023. "Oscillation Criteria for Advanced Half-Linear Differential Equations of Second Order," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
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    8. 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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    10. Taher S. Hassan & Rami Ahmad El-Nabulsi & Naveed Iqbal & Amir Abdel Menaem, 2024. "New Criteria for Oscillation of Advanced Noncanonical Nonlinear Dynamic Equations," Mathematics, MDPI, vol. 12(6), pages 1-13, March.

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