2017/10/24 by Tuen Wai Ng, Ng, Tuen-Wai, Chengfa Wu +1
Mathematics · #30D30 #30D35 #34M05 #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1710.08593
openalex publication_date 2017/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 are at most two. Moreover, for the second order factorizable algebraic ODEs, all the meromorphic solutions of them (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.