On The oscillatory behavior of solutions to a class of second-order nonlinear differential equations

Maged Alkilayh; Maged Alkilayh

doi:10.3934/math.20241718

AIMS Mathematics

2024, Volume 9, Issue 12: 36191-36201. doi: 10.3934/math.20241718

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On The oscillatory behavior of solutions to a class of second-order nonlinear differential equations

Maged Alkilayh ^,

Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

Received: 14 October 2024 Revised: 18 November 2024 Accepted: 29 November 2024 Published: 27 December 2024
MSC : 34C10, 34K11

In this paper, we obtain some oscillatory properties for the noncanonical second-order differential equation with mixed neutral terms. We established our results first by transforming the equation into canonical type and then by using the Riccati technique to get new oscillatory properties for the considered equation. We obtained these results to extend and simplify existing criteria in the literature. We discussed some examples to illustrate the effectiveness of our main results.
- mixed neutral,
- differential equations,
- oscillation conditions,
- second-order,
- delay
Citation: Maged Alkilayh. On The oscillatory behavior of solutions to a class of second-order nonlinear differential equations[J]. AIMS Mathematics, 2024, 9(12): 36191-36201. doi: 10.3934/math.20241718

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Abstract

In this paper, we obtain some oscillatory properties for the noncanonical second-order differential equation with mixed neutral terms. We established our results first by transforming the equation into canonical type and then by using the Riccati technique to get new oscillatory properties for the considered equation. We obtained these results to extend and simplify existing criteria in the literature. We discussed some examples to illustrate the effectiveness of our main results.

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