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Oscillation and Asymptotic Behavior of Third-Order Neutral Delay Differential Equations with Mixed Nonlinearities

Author

Listed:
  • Balakrishnan Sudha

    (Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur 600203, India)

  • George E. Chatzarakis

    (Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, 15122 Marousi, Athens, Greece)

  • Ethiraju Thandapani

    (Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India)

Abstract

In the present article, we create new sufficient conditions for the oscillatory and asymptotic behavior of solutions of third-order nonlinear neutral delay differential equations with several super-linear and sub-linear terms. The results are obtained first by applying the arithmetic–geometric mean inequality along with the linearization method and then using comparison method as well as the integral averaging technique. Finally, we show the importance and novelty of the main results by applying them to special cases of the studied equation.

Suggested Citation

  • Balakrishnan Sudha & George E. Chatzarakis & Ethiraju Thandapani, 2025. "Oscillation and Asymptotic Behavior of Third-Order Neutral Delay Differential Equations with Mixed Nonlinearities," Mathematics, MDPI, vol. 13(5), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:783-:d:1600951
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    References listed on IDEAS

    as
    1. Qing Yang & Xiaojing Wang & Xiwang Cheng & Bo Du & Yuxiao Zhao, 2023. "Positive Periodic Solution for Neutral-Type Integral Differential Equation Arising in Epidemic Model," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    2. Tongxing Li & Chenghui Zhang & Guojing Xing, 2012. "Oscillation of Third-Order Neutral Delay Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-11, January.
    3. 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.
    4. Taher S. Hassan & Bassant M. El-Matary, 2023. "Asymptotic Behavior and Oscillation of Third-Order Nonlinear Neutral Differential Equations with Mixed Nonlinearities," Mathematics, MDPI, vol. 11(2), pages 1-10, January.
    Full references (including those not matched with items on IDEAS)

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