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Erschienen in:
20.07.2018 | Original Research
New oscillation criterion for Emden–Fowler type nonlinear neutral delay differential equations
Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2019
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Abstract
In this paper, we consider the following Emden–Fowler type nonlinear neutral delay differential equations where \(z(t)=y(t)+p(t)y(\tau (t))\). Some new oscillatory and asymptotic properties are obtained by means of the inequality technique and the Riccati transformation. It is worth pointing out that the oscillatory and asymptotic behaviors for our studied equation are ensured by only one condition and \(\alpha \), \(\beta \in \mathbb {R}\) are arbitrary quotients of two odd positive integers, which are completely new compared with previous references. Thus, this paper improves and generalizes some known results. Two illustrative examples are presented at last.
$$\begin{aligned} \left( r(t)(z'(t))^\alpha \right) '+q(t)y^\beta (\sigma (t))=0, \end{aligned}$$