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Multiplicity of Positive Periodic Solutions to Second Order Singular Dynamical Systems

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Abstract

The existence and multiplicity of non-collision periodic solutions for second order singular dynamical systems are discussed in this paper. Using the Green’s function of linear differential equation, we consider general singularity and do not need any kind of strong force condition. The proof relies on a nonlinear alternative principle of Leray–Schauder and a fixed point theorem in cones.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant nos. 11461016 and 11601109), Hainan Natural Science Foundation (Grant no. 117005), China Postdoctoral Science Foundation funded project (Grant no. 2017M612577), Young Foundation of Hainan University (Grant no. hdkyxj201718).

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Authors and Affiliations

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

    Shengjun Li & Yanhua Wang

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

    Shengjun Li

Authors
  1. Shengjun Li
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  2. Yanhua Wang
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Correspondence to Shengjun Li.

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Li, S., Wang, Y. Multiplicity of Positive Periodic Solutions to Second Order Singular Dynamical Systems. Mediterr. J. Math. 14, 202 (2017). https://doi.org/10.1007/s00009-017-1000-0

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  • DOI: https://doi.org/10.1007/s00009-017-1000-0

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