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Asymptotic Behavior of Higher-Order Quasilinear Neutral Differential Equations

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  • Tongxing Li
  • Yuriy V. Rogovchenko

Abstract

We study asymptotic behavior of solutions to a class of higher-order quasilinear neutral differential equations under the assumptions that allow applications to even- and odd-order differential equations with delayed and advanced arguments, as well as to functional differential equations with more complex arguments that may, for instance, alternate indefinitely between delayed and advanced types. New theorems extend a number of results reported in the literature. Illustrative examples are presented.

Suggested Citation

  • Tongxing Li & Yuriy V. Rogovchenko, 2014. "Asymptotic Behavior of Higher-Order Quasilinear Neutral Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, January.
    • Handle: RePEc:hin:jnlaaa:395368
    DOI: 10.1155/2014/395368
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    Cited by:

    1. Jozef Džurina & Said R. Grace & Irena Jadlovská & Tongxing Li, 2020. "Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term," Mathematische Nachrichten, Wiley Blackwell, vol. 293(5), pages 910-922, May.
    2. 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.
    3. 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.
    4. 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.
    5. Grace, Said R. & Jadlovská, Irena & Zafer, Agacik, 2019. "On oscillation of third-order noncanonical delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    6. Zhiyu Zhang & Ruihua Feng & Irena Jadlovská & Qingmin Liu, 2021. "Oscillation Criteria for Third-Order Nonlinear Neutral Dynamic Equations with Mixed Deviating Arguments on Time Scales," Mathematics, MDPI, vol. 9(5), pages 1-18, March.

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