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

  • Hui Li
  • Yige Zhao
  • Zhenlai HanEmail author
Original Research
  • 78 Downloads

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.

Keywords

Oscillation Emden–Fowler Neutral Delay Differential equation 

Mathematics Subject Classification

34C10 34A34 34K40 

Notes

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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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of JinanJinanPeople’s Republic of China

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