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The uniqueness problem and meromorphic solutions of partial differential equations

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Abstract

A general uniqueness theorem is proved for meromorphic functions in Cn which share three distinct small functions with their linear partial differential polynomials. As a consequence, a necessary and sufficient condition in terms of shared values for a meromorphic function to be a solution of a linear partial differential equation of constant coefficients is obtained.

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Author information

Author notes

  1. Der-Chen Chang

    Present address: Department of Mathemaics, Georgetown University, 20057, Washington, DC, USA

Authors and Affiliations

  1. Department of Mathematics, University of Maryland, 20742, College Park, MD, USA

    Carlos A. Berenstein & Der-Chen Chang

  2. Department of Mathematics, Florida International University, 33199, Miami, FL, USA

    Bao Qin Li

Authors
  1. Carlos A. Berenstein
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  2. Der-Chen Chang
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  3. Bao Qin Li
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Additional information

All the three authors are partially supported by NSF grants.

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Berenstein, C.A., Chang, DC. & Li, B.Q. The uniqueness problem and meromorphic solutions of partial differential equations. J. Anal. Math. 77, 51–68 (1999). https://doi.org/10.1007/BF02791257

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  • DOI: https://doi.org/10.1007/BF02791257

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