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Nondegeneracy and Uniqueness of Periodic Solution for a Liénard Equation

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Abstract

In this paper, we consider the nondegeneracy of a Liénard equation

$$\begin{aligned} x''(t)+f(x(t))x'(t)+a(t)x(t)=0. \end{aligned}$$

Besides, by nondegenerate results and Manásevich-Mawhin continuation theorem, we prove the existence and uniqueness of periodic solution of the related Liénard equation.

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Acknowledgements

The authors would like to thank the referee for invaluable comments and insightful suggestions.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454000, China

    Shaowen Yao, Wenjie Li & Zhibo Cheng

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  1. Shaowen Yao
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  2. Wenjie Li
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  3. Zhibo Cheng
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Correspondence to Zhibo Cheng.

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Research is supported by Technological Innovation Talents in Universities and Colleges in Henan Province (21HASTIT025), Natural Science Foundation of Henan Province (222300420449), Innovative Research Team of Henan Polytechnic University (T2022-7) and national natural science foundation of china (11501170).

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Yao, S., Li, W. & Cheng, Z. Nondegeneracy and Uniqueness of Periodic Solution for a Liénard Equation. Qual. Theory Dyn. Syst. 21, 138 (2022). https://doi.org/10.1007/s12346-022-00669-9

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  • DOI: https://doi.org/10.1007/s12346-022-00669-9

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