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New oscillation criterion for Emden–Fowler type nonlinear neutral delay differential equations

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Abstract

In this paper, we consider the following Emden–Fowler type nonlinear neutral delay differential equations

$$\begin{aligned} \left( r(t)(z'(t))^\alpha \right) '+q(t)y^\beta (\sigma (t))=0, \end{aligned}$$

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.

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Acknowledgements

The authors sincerely thank the reviewers for their valuable suggestions and useful comments that have led to the present improved version of the original manuscript. This research is supported by the National Natural Science Foundation of P.R. China (61703180), Natural Science Foundation of Shandong Provincial (ZR2017MA043).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Jinan, Jinan, 250022, Shandong, People’s Republic of China

    Hui Li, Yige Zhao & Zhenlai Han

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  1. Hui Li
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  2. Yige Zhao
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  3. Zhenlai Han
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Correspondence to Zhenlai Han.

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Li, H., Zhao, Y. & Han, Z. New oscillation criterion for Emden–Fowler type nonlinear neutral delay differential equations. J. Appl. Math. Comput. 60, 191–200 (2019). https://doi.org/10.1007/s12190-018-1208-6

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  • DOI: https://doi.org/10.1007/s12190-018-1208-6

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