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A result on the quasi-periodic solutions of forced isochronous oscillators at resonance

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Abstract

In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity

$$x'' + V'(x) + g(x) = e(t,x,x'),$$

where the assumptions on V, g and e are regular, described precisely in the introduction. Using a variant of Moser’s twist theorem of invariant curves, the authors show the existence of quasi-periodic solutions and boundedness of all solutions. This extends the result of Liu to the case of the above system where e depends on the velocity.

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Authors and Affiliations

  1. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Bin Liu & Yingchao Tang

Authors
  1. Bin Liu
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  2. Yingchao Tang
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Corresponding author

Correspondence to Yingchao Tang.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 10325103) and the Chinese Scholarship Council (No. 201206010092).

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Liu, B., Tang, Y. A result on the quasi-periodic solutions of forced isochronous oscillators at resonance. Chin. Ann. Math. Ser. B 36, 523–542 (2015). https://doi.org/10.1007/s11401-015-0912-x

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  • DOI: https://doi.org/10.1007/s11401-015-0912-x

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