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Erschienen in:
2018 | OriginalPaper | Buchkapitel
Oscillation of Sublinear Second Order Neutral Differential Equations via Riccati Transformation
verfasst von : Arun Kumar Tripathy, Abhay Kumar Sethi
Erschienen in: Differential and Difference Equations with Applications
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Abstract
In this work, we establish the necessary conditions for oscillation of the second order neutral delay differential equations of the form: under the assumptions and for various ranges of p(t), where \(0<\gamma \le 1\) is a quotient of odd positive integers.
$$\begin{aligned} (r(t)((x(t)+p(t)x(\tau (t)))')^\gamma )'+q(t) x^\gamma (\sigma (t))+v(t)x^\gamma (\eta (t))=0 \end{aligned}$$
$$\begin{aligned} \int _{0}^{\infty }\left( \frac{1}{r(t)}\right) ^\frac{1}{\gamma }dt= & {} \infty \end{aligned}$$
$$\begin{aligned} \int _{0}^{\infty }\left( \frac{1}{r(t)}\right) ^\frac{1}{\gamma }dt< & {} \infty \end{aligned}$$