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

John R. Graef, Said R. Grace, Irena Jadlovská () and Ercan Tunç
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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

Mathematics, 2022, vol. 10, issue 16, 1-11

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.

Keywords: oscillation; asymptotic behavior; higher-order; nonlinear neutral term (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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