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On unicity of meromorphic solutions to difference Painlevé equation
Author(s) -
Lü Feng,
Wang Yanfeng,
Lü Weiran
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4802
Subject(s) - meromorphic function , mathematics , uniqueness , elliptic function , uniqueness theorem for poisson's equation , order (exchange) , function (biology) , pure mathematics , nevanlinna theory , mathematical analysis , finance , evolutionary biology , economics , biology
In this paper, we consider the uniqueness problems of finite‐order meromorphic solutions to Painlevé equation. Our result says that such solutions w are uniquely determined by their poles and the zeros of w − e j (counting multiplicities) for 2 finite complex numbers e 1 ≠ e 2 . As applications, we derive 2 uniqueness theorems about the Weierstrass ℘ function and Jacobi elliptic function s n , respectively.