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New Oscillation Results for Third-Order Half-Linear Neutral Differential Equations

Author

Listed:
  • K. S. Vidhyaa

    (Department of Mathematics, SRM Easwari Engineering College, Ramapuram, Chennai, Tamil Nadu 600 089, India)

  • John R. Graef

    (Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403-2598, USA)

  • E. Thandapani

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

Abstract

The main purpose of this paper is to obtain criteria for the oscillation of all solutions of a third-order half-linear neutral differential equation. The main result in this paper is an oscillation theorem obtained by comparing the equation under investigation to two first order linear delay differential equations. An additional result is obtained by using a Riccati transformation technique. Examples are provided to show the importance of the main results.

Suggested Citation

  • K. S. Vidhyaa & John R. Graef & E. Thandapani, 2020. "New Oscillation Results for Third-Order Half-Linear Neutral Differential Equations," Mathematics, MDPI, vol. 8(3), pages 1-9, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:325-:d:327129
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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. George E. Chatzarakis & Said R. Grace & Irena Jadlovská & Tongxing Li & Ercan Tunç, 2019. "Oscillation Criteria for Third-Order Emden–Fowler Differential Equations with Unbounded Neutral Coefficients," Complexity, Hindawi, vol. 2019, pages 1-7, August.
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