Some Results on the Painlevé III Difference Equations with Constant Coefficients

Lei Liu; Jilong Zhang

doi:10.3103/S1068362320020065

Some Results on the Painlevé III Difference Equations with Constant Coefficients

Lei Liu^*
, Jilong Zhang^*

^*此作品的通讯作者

数学科学学院

Beihang University

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

Abstract: In this paper, we investigate the following two Painlevé III equations: (Formula presented.). and (Formula presented.)., where (Formula presented.). and (Formula presented.). and λ /∈ {±1} are constants. We discuss the questions of existence of rational solutions, of Borel exceptional values and the exponents of convergence of zeros, poles and fixed points of transcendental meromorphic solutions of these equations.

源语言	英语
页（从-至）	115-125
页数	11
期刊	Journal of Contemporary Mathematical Analysis
卷	55
期	2
DOI	https://doi.org/10.3103/S1068362320020065
出版状态	已出版 - 1 3月 2020

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title = "Some Results on the Painlev{\'e} III Difference Equations with Constant Coefficients",

abstract = "Abstract: In this paper, we investigate the following two Painlev{\'e} III equations: (Formula presented.). and (Formula presented.)., where (Formula presented.). and (Formula presented.). and λ /∈ \{±1\} are constants. We discuss the questions of existence of rational solutions, of Borel exceptional values and the exponents of convergence of zeros, poles and fixed points of transcendental meromorphic solutions of these equations.",

keywords = "Painlev{\'e} difference equation, finite order, meromorphic solution",

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AU - Zhang, Jilong

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N2 - Abstract: In this paper, we investigate the following two Painlevé III equations: (Formula presented.). and (Formula presented.)., where (Formula presented.). and (Formula presented.). and λ /∈ {±1} are constants. We discuss the questions of existence of rational solutions, of Borel exceptional values and the exponents of convergence of zeros, poles and fixed points of transcendental meromorphic solutions of these equations.

AB - Abstract: In this paper, we investigate the following two Painlevé III equations: (Formula presented.). and (Formula presented.)., where (Formula presented.). and (Formula presented.). and λ /∈ {±1} are constants. We discuss the questions of existence of rational solutions, of Borel exceptional values and the exponents of convergence of zeros, poles and fixed points of transcendental meromorphic solutions of these equations.

KW - Painlevé difference equation

KW - finite order

KW - meromorphic solution

UR - https://www.scopus.com/pages/publications/85090051118

U2 - 10.3103/S1068362320020065

DO - 10.3103/S1068362320020065

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VL - 55

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JO - Journal of Contemporary Mathematical Analysis

JF - Journal of Contemporary Mathematical Analysis

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ER -

Some Results on the Painlevé III Difference Equations with Constant Coefficients

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