Second order neutral delay differential equations: on oscillation via linearization

Pakize Temtek; Nagehan Kılınç Geçer; Pakize Temtek; Nagehan Kılınç Geçer

doi:10.3934/math.2026848

AIMS Mathematics

2026, Volume 11, Issue 7: 20899-20914. doi: 10.3934/math.2026848

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Research article

Second order neutral delay differential equations: on oscillation via linearization

Pakize Temtek ^{1
,
,},
Nagehan Kılınç Geçer ²

1.
Department of Mathematics, Faculty of Sciences, Erciyes University, Kayseri, 38030, Turkey
2.
Department of Mathematics, Faculty of Arts and Sciences, Kırşehir Ahi Evran University, Kırşehir 40100, Turkey

Received: 07 April 2026 Revised: 30 June 2026 Accepted: 08 July 2026 Published: 15 July 2026
MSC : 34K40, 34K25, 34K06, 34K11

This paper investigates the oscillatory behavior of second-order neutral differential equations with a continuously distributed delay. New monotonic characteristics of non-oscillatory solutions of the considered neutral delay differential equation are established. We obtain new oscillation criteria by using these properties to linearize the problem and applying the comparison principle. The corresponding proofs are established under the canonical assumption. The results in this paper improve and generalize some known results in the existing works. Finally, numerical validation via illustrative examples are provided.
- second-order neutral delay differential equations,
- asymptotic properties,
- linearization,
- oscillation theory
Citation: Pakize Temtek, Nagehan Kılınç Geçer. Second order neutral delay differential equations: on oscillation via linearization[J]. AIMS Mathematics, 2026, 11(7): 20899-20914. doi: 10.3934/math.2026848

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Abstract

This paper investigates the oscillatory behavior of second-order neutral differential equations with a continuously distributed delay. New monotonic characteristics of non-oscillatory solutions of the considered neutral delay differential equation are established. We obtain new oscillation criteria by using these properties to linearize the problem and applying the comparison principle. The corresponding proofs are established under the canonical assumption. The results in this paper improve and generalize some known results in the existing works. Finally, numerical validation via illustrative examples are provided.

References

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