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Periodic orbits of a singular superlinear planar system

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Abstract

We present a planar system which depends periodically on time. If the force admits a repulsive singularity and a superlinear growth, we show that such a system has a family of periodic orbits rotating around the origin with angular momentum from zero to infinity.

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Acknowledgments

We would like to show our great thanks to the anonymous referee for his/her valuable suggestions and comments. We declare that three authors have the same contribution to this work.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Hohai University, Nanjing, 210098, China

    Jifeng Chu & Shengjun Li

  2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    Ming Li

Authors
  1. Jifeng Chu
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  2. Ming Li
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  3. Shengjun Li
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Corresponding author

Correspondence to Jifeng Chu.

Additional information

Communicated by A. Constantin.

Jifeng Chu was supported by the National Natural Science Foundation of China (Grant No. 11171090 and No. 11271333) and the Fundamental Research Funds for the Central Universities (Grant No. 2015B19214). Ming Li was supported by the National Science Foundation of China (Grant No. 11571188). Shengjun Li was supported by the National Natural Science Foundation of China (Grant No. 11461016).

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Chu, J., Li, M. & Li, S. Periodic orbits of a singular superlinear planar system. Monatsh Math 181, 71–87 (2016). https://doi.org/10.1007/s00605-015-0835-3

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  • DOI: https://doi.org/10.1007/s00605-015-0835-3

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