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Non-degeneracy and Uniqueness of Periodic Solutions for a Liénard Equation with a Linear Difference Operator

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Abstract

In this paper, we investigate the non-degeneracy of a Liénard equation with a linear difference operator by means of the generalized Wirtinger inequality. In addition, by the non-degenerate results and an extension of Mawhin’s continuation theorem, the existence and uniqueness of periodic solutions for a Liénard equation with a linear difference operator are proved.

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Authors and Affiliations

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

    Zhibo Cheng & Yafei Li

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  1. Zhibo Cheng
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  2. Yafei Li
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Z.B. Cheng and Y.F. Li wrote the main manuscript text. All authors reviewed the manuscript.

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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), Henan Province “Double first-class" discipline establishment engineering cultivation project (AQ20230718) and Innovative Research Team of Henan Polytechnic University (T2022-7).

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Cheng, Z., Li, Y. Non-degeneracy and Uniqueness of Periodic Solutions for a Liénard Equation with a Linear Difference Operator. Qual. Theory Dyn. Syst. 23, 142 (2024). https://doi.org/10.1007/s12346-024-00973-6

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