Ukrainian Mathematical Journal

, Volume 58, Issue 4, pp 487–504 | Cite as

On Dirichlet problem for string equation, Poncelet problem, Pell-Abel equation, and some other related problems

  • V. P. Burskii
  • A. S. Zhedanov


In a plane domain bounded by a biquadratic curve, we consider the problem of the uniqueness of a solution of the Dirichlet problem for the string equation. We show that this problem is equivalent to the classical Poncelet problem in projective geometry for two appropriate ellipses and also to the problem of the solvability of the Pell-Abel algebraic equation; some other related problems are also considered.


Dirichlet Problem Periodic Point Moment Problem Projective Transformation String Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. P. Burskii
    • 1
  • A. S. Zhedanov
    • 2
  1. 1.Institute of Applied Mathematics and MechanicsUkrainian Academy of SciencesDonetsk
  2. 2.Donetsk Physicotechnical InstituteUkrainian Academy of SciencesDonetsk

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