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Some New Oscillation Results for Higher-Order Nonlinear Differential Equations with a Nonlinear Neutral Term

Author

Listed:
  • John R. Graef

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

  • Said R. Grace

    (Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Giza 12221, Egypt)

  • Irena Jadlovská

    (Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01 Košice, Slovakia)

  • Ercan Tunç

    (Department of Mathematics, Faculty of Arts and Sciences, Tokat Gaziosmanpasa University, Tokat 60240, Turkey)

Abstract

The authors study the oscillatory behaviors of solutions of higher-order nonlinear differential equations with a nonlinear neutral term. The right hand side of their equation contains both an advanced and a delay term, and either (or both) of them can be sublinear or superlinear. The influence of these terms on the oscillatory and asymptotic behaviors of solutions is investigated by using a comparison to first-order advanced and delay differential equations. New oscillation criteria are presented that improve and extend many known oscillation criteria in the literature. An example is provided to illustrate the results.

Suggested Citation

  • John R. Graef & Said R. Grace & Irena Jadlovská & Ercan Tunç, 2022. "Some New Oscillation Results for Higher-Order Nonlinear Differential Equations with a Nonlinear Neutral Term," Mathematics, MDPI, vol. 10(16), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2997-:d:892617
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    References listed on IDEAS

    as
    1. Shao-Yan Zhang & Qi-Ru Wang, 2012. "Oscillation Criteria for Second-Order Nonlinear Dynamic Equations on Time Scales," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-20, November.
    2. Tongxing Li & Yuriy V. Rogovchenko, 2014. "Oscillation Theorems for Second-Order Nonlinear Neutral Delay Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, June.
    3. Osama Moaaz & Dimplekumar Chalishajar & Omar Bazighifan, 2019. "Some Qualitative Behavior of Solutions of General Class of Difference Equations," Mathematics, MDPI, vol. 7(7), pages 1-12, July.
    Full references (including those not matched with items on IDEAS)

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