Second order neutral multi-delay differential equations and its oscillatory criteria derived by linearization

Pakize Temtek; Pakize Temtek

doi:10.3934/math.20251105

AIMS Mathematics

2025, Volume 10, Issue 10: 24971-24982. doi: 10.3934/math.20251105

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Research article

Second order neutral multi-delay differential equations and its oscillatory criteria derived by linearization

Pakize Temtek ^,

Department of Mathematics, Faculty of Sciences, Erciyes University, Melikgazi 38030, Turkey

Received: 18 August 2025 Revised: 13 October 2025 Accepted: 16 October 2025 Published: 30 October 2025
MSC : 34K40, 34K25, 34K06, 34K11

In this paper, we investigate the oscillatory behavior of second-order neutral multi-delay differential equations
$ \begin{equation*} \left( r \left({t}\right)\left[\left( u\left({t}\right) + \sum\limits_{i = 1}^nb_i(t)u(\psi_i(t))\right)'\right]^{\alpha}\right)^\prime + Q\left({t}, u\left( \tau \left({t}\right)\right)\right) = 0. \end{equation*} $
We introduce new monotonic properties of the non-oscillatory solutions of the equation, which are then used to linearize the equation and derive new oscillatory criteria. Our results are further supported by a numerical simulation example.
- second-order neutral multi-delay differential equations,
- asymptotic properties,
- linearization,
- oscillation theory
Citation: Pakize Temtek. Second order neutral multi-delay differential equations and its oscillatory criteria derived by linearization[J]. AIMS Mathematics, 2025, 10(10): 24971-24982. doi: 10.3934/math.20251105

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Abstract

In this paper, we investigate the oscillatory behavior of second-order neutral multi-delay differential equations

$ \begin{equation*} \left( r \left({t}\right)\left[\left( u\left({t}\right) + \sum\limits_{i = 1}^nb_i(t)u(\psi_i(t))\right)'\right]^{\alpha}\right)^\prime + Q\left({t}, u\left( \tau \left({t}\right)\right)\right) = 0. \end{equation*} $

We introduce new monotonic properties of the non-oscillatory solutions of the equation, which are then used to linearize the equation and derive new oscillatory criteria. Our results are further supported by a numerical simulation example.

References

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