Littlewood Problem for a Singular Subquadratic Potential

  • Xiong LiEmail author
  • Yingfei Yi
Part of the Fields Institute Communications book series (FIC, volume 64)


We consider a periodically forced singular oscillator in which the potential has subquadratic growth at infinity and admits a singularity. Using Moser’s twist theorem of invariant curves, we show the existence of quasiperiodic solutions. This solves the Littlewood problem on the boundedness of all solutions for such a system.



Xiong Li was supported in part by NSFC(11031002), the Fundamental Research Funds for the Central Universities and SRF for ROCS, SEM Yingfei Yi was supported in part by NSF grant DMS0708331, NSFC Grant 10428101, and a Changjiang Scholarship from Jilin University.

Received 9/20/2009; Accepted 8/1/2010


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesBeijing Normal UniversityBeijingPR China
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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