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Israel Journal of Mathematics

, Volume 229, Issue 1, pp 1–38 | Cite as

Nonlinear Loewy factorizable algebraic ODEs and Hayman’s conjecture

  • Tuen-Wai NgEmail author
  • Cheng-Fa Wu
Article
  • 44 Downloads

Abstract

In this paper, we introduce certain n-th order nonlinear Loewy factorizable algebraic ordinary differential equations for the first time and study the growth of their meromorphic solutions in terms of the Nevanlinna characteristic function. It is shown that for generic cases all their meromorphic solutions are elliptic functions or their degenerations and hence their order of growth is at most two. Moreover, for the second order factorizable algebraic ODEs, all their meromorphic solutions (except for one case) are found explicitly. This allows us to show that a conjecture proposed by Hayman in 1996 holds for these second order ODEs.

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Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Department of MathematicsThe University of Hong KongPokfulamHong Kong
  2. 2.Institute for Advanced StudyShenzhen UniversityShenzhenPR China

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