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Periodic Solutions of Discontinuous Duffing Equations

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Abstract

In this paper, we investigate the multiplicity problem of periodic solutions for a class of periodically forced Duffing equations allowing for discontinuities. By using a generalized form of the Poincaré–Birkhoff theorem due to Ding (Proc Am Math Soc 88:341–346, 1983), we demonstrate that the discontinuous equation has an infinite number of periodic solutions with large amplitude.

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Acknowledgements

The author would like to give her sincere thanks to the reviewers for their careful suggestions and helpful comments. With these suggestions and comments, the author improves her manuscript greatly. This work is supported by National Natural Science Foundation of China (11701224) and Natural Science Foundation of JiangSu Province Youth Foundation (BK20170168).

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  1. School of Science, Jiangnan University, Wuxi, 214122, China

    Fangfang Jiang

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Correspondence to Fangfang Jiang.

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Jiang, F. Periodic Solutions of Discontinuous Duffing Equations. Qual. Theory Dyn. Syst. 19, 93 (2020). https://doi.org/10.1007/s12346-020-00428-8

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