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Third-Order Noncanonical Neutral Delay Differential Equations: Nonexistence of Kneser Solutions via Myshkis Type Criteria

Author

Listed:
  • Gunasekaran Nithyakala

    (Department of Applied Mathematics and Computational Science, Thiagarajar College of Engineering, Madurai 625 015, Tamilnadu, India)

  • George E. Chatzarakis

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

  • Govindasamy Ayyappan

    (Department of Mathematics, Government Arts and Science College, Pappireddipatti 636 905, Tamilnadu, India)

  • Ethiraju Thandapani

    (Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005, Tamilnadu, India)

Abstract

The purpose of this paper is to add some new asymptotic and oscillatory results for third-order neutral delay differential equations with noncanonical operators. Without assuming any extra conditions, by using the canonical transform technique, the studied equation is changed to a canonical type equation, and this reduces the number of classes of nonoscillatory solutions into two instead of four. Then, we obtain Myshkis type sufficient conditions for the nonexistence of Kneser type solutions for the studied equation. Finally, employing these newly obtained criteria, we provide conditions for the oscillation of all solutions of the studied equation. Examples are presented to illustrate the importance and the significance of the main results.

Suggested Citation

  • Gunasekaran Nithyakala & George E. Chatzarakis & Govindasamy Ayyappan & Ethiraju Thandapani, 2024. "Third-Order Noncanonical Neutral Delay Differential Equations: Nonexistence of Kneser Solutions via Myshkis Type Criteria," Mathematics, MDPI, vol. 12(18), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2847-:d:1477545
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    References listed on IDEAS

    as
    1. 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.
    2. Džurina, Jozef & Jadlovská, Irena, 2018. "Oscillation of third-order differential equations with noncanonical operators," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 394-402.
    3. 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.
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