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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 3

Oscillation theorems for second-order nonlinear delay differential equations of neutral type

Başak Karpuz0000-0002-0242-972X
Shyam S. Santra0000-0001-9740-3081
Sayfa
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Yayın Tarihi
2019-06-15
DOI
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Further, some illustrative examples showing applicability of the new results are included.

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Amaç & Hipotez:In this paper, new sufficient conditions are obtained for oscillation of second-order neutral delay differential equations of the form \[\frac{d}{dt}\bigg[r(t)\frac{d}{dt}[x(t)+p(t)x(\tau(t))]\bigg]+q(t)G\bigl(x(\sigma(t))\bigr)=0\: for\: t\geq t_{0},\] under the assumptions $\int^{\infty}\frac{1}{r(\eta)}d\eta=\infty$ and $\int^{\infty}\frac{1}{r(\eta)}d\eta<\infty$ for various ranges of the bounded neutral coefficient $p$.
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Temel Bulgular & Veri:Unlike most of the previous results, $\tau^{\prime}$ is allowed to be oscillatory.
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Sonuç & Katkı:Further, some illustrative examples showing applicability of the new results are included.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Oscillation · nonoscillation · nonlinear

Abstract

In this paper, new sufficient conditions are obtained for oscillation of second-order neutral delay differential equations of the form \[\frac{d}{dt}\bigg[r(t)\frac{d}{dt}[x(t)+p(t)x(\tau(t))]\bigg]+q(t)G\bigl(x(\sigma(t))\bigr)=0\: for\: t\geq t_{0},\] under the assumptions $\int^{\infty}\frac{1}{r(\eta)}d\eta=\infty$ and $\int^{\infty}\frac{1}{r(\eta)}d\eta<\infty$ for various ranges of the bounded neutral coefficient $p$. Unlike most of the previous results, $\tau^{\prime}$ is allowed to be oscillatory. Further, some illustrative examples showing applicability of the new results are included.

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Bu Makaleye Atıf Yap

Karpuz, B., Santra, S. S. (2019). Oscillation theorems for second-order nonlinear delay differential equations of neutral type. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 3. https://ajindex.com/articles/1402779

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Kaynakça (17)

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