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Oscillation criteria for second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients on time scales

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Abstract

We investigate oscillation of certain second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients. We use some different techniques and apply Riccati transformation to establish new oscillatory criteria which include two necessary and sufficient conditions. Moreover, we point out that how the power γ plays its role. Some interesting examples are given to illustrate the versatility of our results.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11271379) and Guangzhou Postdoctoral Science Research Foundation Project (Grant No. gdbsh2014003).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    XunHuan Deng & Zhan Zhou

  2. Key Laboratory of Mathematics and Interdisciplinary Science of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, 510006, China

    XunHuan Deng & Zhan Zhou

  3. School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou, 510275, China

    QiRu Wang

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  1. XunHuan Deng
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  2. QiRu Wang
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  3. Zhan Zhou
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Correspondence to XunHuan Deng.

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Deng, X., Wang, Q. & Zhou, Z. Oscillation criteria for second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients on time scales. Sci. China Math. 60, 113–132 (2017). https://doi.org/10.1007/s11425-016-0070-y

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  • DOI: https://doi.org/10.1007/s11425-016-0070-y

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