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Oscillation of Second-Order Emden–Fowler Neutral Differential Equations with Advanced and Delay Arguments

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Abstract

In this paper, we study the oscillation of the second-order Emden–Fowler neutral differential equations with advanced and delay arguments

$$\begin{aligned} (r(t)(x(t)+p(t)x(\tau (t)))')'+q(t)x^\gamma (\sigma (t))=0,\ \quad t\geqslant t_0, \end{aligned}$$

where \(\tau (t)\leqslant t\), \(\sigma (t)\geqslant t\). Sufficient conditions for oscillation of the equation are obtained by using the inequality principle, comparison principle and Riccati transform. Two examples are given to illustrate the results.

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Authors and Affiliations

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

    Limei Feng & Shurong Sun

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  1. Limei Feng
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  2. Shurong Sun
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Correspondence to Shurong Sun.

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Communicated by Shangjiang Guo.

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This research is supported by the Natural Science Foundation of China (61703180, 61803176), and supported by Shandong Provincial Natural Science Foundation (ZR2016AM17, ZR2017MA043).

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Feng, L., Sun, S. Oscillation of Second-Order Emden–Fowler Neutral Differential Equations with Advanced and Delay Arguments. Bull. Malays. Math. Sci. Soc. 43, 3777–3790 (2020). https://doi.org/10.1007/s40840-020-00901-2

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  • DOI: https://doi.org/10.1007/s40840-020-00901-2

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