Investigation of the impact of delayed damping on the asymptotic behavior of solutions to Emden–Fowler neutral differential equations

Osama Moaaz; Wedad Albalawi; Osama Moaaz; Wedad Albalawi

doi:10.3934/math.20251106

AIMS Mathematics

2025, Volume 10, Issue 10: 24983-24996. doi: 10.3934/math.20251106

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Investigation of the impact of delayed damping on the asymptotic behavior of solutions to Emden–Fowler neutral differential equations

Osama Moaaz ^1,2,
Wedad Albalawi ^{3
,
,}

1.
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
3.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Received: 10 August 2025 Revised: 14 October 2025 Accepted: 21 October 2025 Published: 31 October 2025
MSC : 34C10, 34K11

This paper examines the oscillatory behavior of solutions to Emden–Fowler neutral differential equations that incorporate a delayed damping term. To our knowledge, there are no prior results addressing the impact of delayed damping on the oscillatory behavior of neutral equations. We establish a new sufficient criterion to confirm that non-oscillatory solutions exhibit asymptotic behavior. Then, we refine and extend this criterion to include the ordinary case. Applying our results to an Euler-type equation shows that they are an extension and complement to the results reported in the literature.
- differential equations,
- a delayed damping term,
- Emden–Fowler equations,
- neutral equation,
- asymptotic properties
Citation: Osama Moaaz, Wedad Albalawi. Investigation of the impact of delayed damping on the asymptotic behavior of solutions to Emden–Fowler neutral differential equations[J]. AIMS Mathematics, 2025, 10(10): 24983-24996. doi: 10.3934/math.20251106

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Abstract

This paper examines the oscillatory behavior of solutions to Emden–Fowler neutral differential equations that incorporate a delayed damping term. To our knowledge, there are no prior results addressing the impact of delayed damping on the oscillatory behavior of neutral equations. We establish a new sufficient criterion to confirm that non-oscillatory solutions exhibit asymptotic behavior. Then, we refine and extend this criterion to include the ordinary case. Applying our results to an Euler-type equation shows that they are an extension and complement to the results reported in the literature.

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