On unicity of meromorphic solutions to difference Painlevé equation

摘要

> 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.