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Journal of Mathematical Sciences

, Volume 173, Issue 2, pp 201–206 | Cite as

Unicity of meromorphic solutions of partial differential equations

  • Pei-Chu Hu
  • Bao-Qin Li
Article

Abstract

In this survey, results on the existence, growth, uniqueness, and value distribution of meromorphic (or entire) solutions of linear partial differential equations of the second order with polynomial coefficients that are similar or different from that of meromorphic solutions of linear ordinary differential equations have been obtained. We have characterized those entire solutions of a special partial differential equation that relate to Jacobian polynomials. We prove a uniqueness theorem of meromorphic functions of several complex variables sharing three values taking into account multiplicity such that one of the meromorphic functions satisfies a nonlinear partial differential equations of the first order with meromorphic coefficients, which extends the Brosch’s uniqueness theorem related to meromorphic solutions of nonlinear ordinary differential equations of the first order.

Keywords

Entire Function Jacobian Polynomial Entire Solution Nonlinear Ordinary Differential Equation Meromorphic Solution 
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. 2011

Authors and Affiliations

  1. 1.Department of MathematicsShandong UniversityShandongP. R. China
  2. 2.Department of MathematicsFlorida International UniversityMiamiUSA

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