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Periodic Solutions for a Class of n-dimensional Prescribed Mean Curvature Equations

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Abstract

In this paper, by using an extension of Mawhin’s continuation theorem and some analysis methods, we study the existence of periodic solutions for the following prescribed mean curvature system

$$\frac{d}{{dt}}\varphi \left( {x'} \right) + \nabla W\left( x \right) = p\left( t \right),$$

where x ∊ ℝn, W ∊ C1(ℝn, ℝ), p ∊ C(ℝ, ℝn) is T-periodic and

$$\varphi \left( x \right)\frac{x}{{\sqrt {1 + |x{|^2}} }}.$$

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Acknowledgments

We would like to express our great thanks to the referees for their valuable suggestions.

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Authors and Affiliations

  1. School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, 232001, China

    Zai-tao Liang

  2. College of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing, 210044, China

    Shi-ping Lu

Authors
  1. Zai-tao Liang
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  2. Shi-ping Lu
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Corresponding author

Correspondence to Zai-tao Liang.

Additional information

Zaitao Liang was supported by the National Natural Science Foundation of China (No. 11901004), the Natural Science Foundation of Anhui Province (No. 1908085QA02) and the Key Program of Scientific Research Fund for Young Teachers of AUST (No. QN2018109). Shiping Lu was sponsored by the National Natural Science Foundation of China (No. 11271197).

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Liang, Zt., Lu, Sp. Periodic Solutions for a Class of n-dimensional Prescribed Mean Curvature Equations. Acta Math. Appl. Sin. Engl. Ser. 36, 516–526 (2020). https://doi.org/10.1007/s10255-020-0943-2

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  • DOI: https://doi.org/10.1007/s10255-020-0943-2

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