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2018•Mathematical Methods in the Applied SciencesRequires access

On unicity of meromorphic solutions to difference Painlevé equation

Feng Lü, Yanfeng Wang, Weiran Lü

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Abstract

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−ej (counting multiplicities) for 2 finite complex numbers e1≠e2. As applications, we derive 2 uniqueness theorems about the Weierstrass ℘ function and Jacobi elliptic function sn, respectively.

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What this paper is about

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−ej (counting multiplicities) for 2 finite complex numbers e1≠e2. As applications, we derive 2 uniqueness theorems about the Weierstrass ℘ function and Jacobi elliptic function sn, respectively.

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Available abstract

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−ej (counting multiplicities) for 2 finite complex numbers e1≠e2. As applications, we derive 2 uniqueness theorems about the Weierstrass ℘ function and Jacobi elliptic function sn, respectively.

Key concepts: Meromorphic function, Mathematics, Uniqueness, Elliptic function, Uniqueness theorem for Poisson's equation, Order (exchange), Function (biology), Pure mathematics

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