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^*

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	115-125
Number of pages	11
Journal	Journal of Contemporary Mathematical Analysis
Volume	55
Issue number	2
DOIs	https://doi.org/10.3103/S1068362320020065
State	Published - 1 Mar 2020

Keywords

Painlevé difference equation
finite order
meromorphic solution

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10.3103/S1068362320020065

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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.",

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author = "Lei Liu and Jilong Zhang",

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Y1 - 2020/3/1

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

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DO - 10.3103/S1068362320020065

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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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Keywords

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