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On the oscillation of second-order Emden-Fowler neutral differential equations

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Abstract

In this paper, we study the following second-order Emden-Fowler neutral delay differential equation

$$(r(t)z'(t) )'+q(t)|x(\sigma(t))|^{\gamma-1}x(\sigma(t))=0,$$

where \(z(t)=x(t)+p(t)x(t-\tau),\ \int_{t_{0}}^{\infty}\frac{1}{r(t)}\mathrm{d}t<\infty\). We establish some new oscillation results which handle some cases not covered by known criteria.

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Authors and Affiliations

  1. School of Science, University of Jinan, Jinan, Shandong, 250022, P.R. China

    Tongxing Li, Zhenlai Han & Shurong Sun

  2. School of Control Science and Engineering, Shandong University, Jinan, Shandong, 250061, P.R. China

    Tongxing Li, Zhenlai Han & Chenghui Zhang

  3. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, 65409-0020, USA

    Shurong Sun

Authors
  1. Tongxing Li
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  2. Zhenlai Han
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  3. Chenghui Zhang
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  4. Shurong Sun
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Corresponding author

Correspondence to Zhenlai Han.

Additional information

This research is supported by the Natural Science Foundation of China (60774004, 60904024), China Postdoctoral Science Foundation Funded Project (20080441126, 200902564), Shandong Postdoctoral Funded Project (200802018), the Natural Science Foundation of Shandong (Y2008A28, ZR2009AL003), and University of Jinan Research Funds for Doctors (XBS0843).

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Li, T., Han, Z., Zhang, C. et al. On the oscillation of second-order Emden-Fowler neutral differential equations. J. Appl. Math. Comput. 37, 601–610 (2011). https://doi.org/10.1007/s12190-010-0453-0

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  • DOI: https://doi.org/10.1007/s12190-010-0453-0

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