Second-order general Emden-Fowler differential equations of neutral type: Improved Kamenev-type oscillation criteria

Asma Al-Jaser; Osama Moaaz; Asma Al-Jaser; Osama Moaaz

doi:10.3934/era.2024241

Electronic Research Archive

2024, Volume 32, Issue 9: 5231-5248. doi: 10.3934/era.2024241

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Research article

Second-order general Emden-Fowler differential equations of neutral type: Improved Kamenev-type oscillation criteria

Asma Al-Jaser ^{1
,
,},
Osama Moaaz ^{2
,
,}

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia

Received: 10 July 2024 Revised: 07 August 2024 Accepted: 28 August 2024 Published: 09 September 2024

The study of the oscillatory behavior of a general class of neutral Emden-Fowler differential equations is the focus of this work. The main motivations for studying the oscillatory behavior of neutral equations are their many applications as well as the richness of these equations with exciting analytical issues. We obtained novel oscillation conditions in Kamenev-type criteria for the considered equation in the canonical case. We improve the monotonic and asymptotic characteristics of the non-oscillatory solutions to the considered equation and then utilize these characteristics to refine the oscillation conditions. We present, through examples and discussions, what demonstrates the novelty and efficiency of the results compared to previous relevant findings in the literature. In addition, we numerically represent the solutions of some special cases to support the theoretical results.
- differential equations,
- Kamenev-type criteria,
- oscillation theory,
- canonical case,
- neutral argument
Citation: Asma Al-Jaser, Osama Moaaz. Second-order general Emden-Fowler differential equations of neutral type: Improved Kamenev-type oscillation criteria[J]. Electronic Research Archive, 2024, 32(9): 5231-5248. doi: 10.3934/era.2024241

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Abstract

The study of the oscillatory behavior of a general class of neutral Emden-Fowler differential equations is the focus of this work. The main motivations for studying the oscillatory behavior of neutral equations are their many applications as well as the richness of these equations with exciting analytical issues. We obtained novel oscillation conditions in Kamenev-type criteria for the considered equation in the canonical case. We improve the monotonic and asymptotic characteristics of the non-oscillatory solutions to the considered equation and then utilize these characteristics to refine the oscillation conditions. We present, through examples and discussions, what demonstrates the novelty and efficiency of the results compared to previous relevant findings in the literature. In addition, we numerically represent the solutions of some special cases to support the theoretical results.

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