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A priori bounds for periodic solutions of a Duffing equation

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Abstract

In this paper a well known Duffing type equation is considered. By means of a Liapunov function and careful estimation, we establish a priori bounds for periodic solutions and their derived functions. Coincidence theorems can then be applied to yield sufficient conditions for the existence of periodic solutions. Our conclusion improve several well known results in the literature.

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Authors and Affiliations

  1. Department of Mathematics, Shaoyang University, Hunan, 422000, People’s Republic of China

    Xinmin Wu & Jingwen Li

  2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, 411105, People’s Republic of China

    Yong Zhou

Authors
  1. Xinmin Wu
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  2. Jingwen Li
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  3. Yong Zhou
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Corresponding author

Correspondence to Yong Zhou.

Additional information

Research supported by Specialized Research Fund for the Doctoral Program of Higher Education (20060530001).

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Wu, X., Li, J. & Zhou, Y. A priori bounds for periodic solutions of a Duffing equation. J. Appl. Math. Comput. 26, 535–543 (2008). https://doi.org/10.1007/s12190-007-0024-1

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  • DOI: https://doi.org/10.1007/s12190-007-0024-1

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