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Applications of Schauder’s fixed point theorem to singular radially symmetric systems

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Abstract

We study the existence of periodic orbits of radially symmetric systems with a repulsive singularity. We show that such a system has a family of orbits rotating around the origin with small angular momentum. Our proofs are based on the use of topological degree theory and Schauder’s fixed point theorem.

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Authors and Affiliations

  1. College of Information Sciences and Technology, Hainan University, Haikou, 570228, China

    Shengjun Li

  2. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, China

    Shengjun Li & Xianhua Tang

  3. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Huxiao Luo

Authors
  1. Shengjun Li
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  2. Xianhua Tang
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  3. Huxiao Luo
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Correspondence to Shengjun Li.

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This work is supported by the National Natural Science Foundation of China (Grant nos. 11861028 and 11461016), Hainan Natural Science Foundation (Grant no. 117005), Young Foundation of Hainan University (Grant no. hdkyxj201718).

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Li, S., Tang, X. & Luo, H. Applications of Schauder’s fixed point theorem to singular radially symmetric systems. J. Fixed Point Theory Appl. 21, 46 (2019). https://doi.org/10.1007/s11784-019-0682-2

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  • DOI: https://doi.org/10.1007/s11784-019-0682-2

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