On Uniqueness of Meromorphic Solutions to Some Differential-Difference Equations

Z. Sui; J. Zhang

doi:10.3103/S1068362325700232

On Uniqueness of Meromorphic Solutions to Some Differential-Difference Equations

Z. Sui^*
, J. Zhang^*

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

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

Abstract

Abstract: In this paper, we prove the uniqueness of finite-order transcendental meromorphic solutions of differential-difference Painlevé III and V equations: (Formula presented.) and (Formula presented.) where, and are small functions of solution. We show that if the solution shares,, and CM with another meromorphic function, then. Moreover, for Painlevé V equation, if is replaced by, it is sufficient for and to share the values and CM. MSC2020 numbers:30D35.

Original language	English
Pages (from-to)	61-72
Number of pages	12
Journal	Journal of Contemporary Mathematical Analysis
Volume	61
Issue number	1
DOIs	https://doi.org/10.3103/S1068362325700232
State	Published - Feb 2026

Keywords

Nevanlinna’s theory
differential-difference equation
meromorphic function
uniqueness

Access to Document

10.3103/S1068362325700232

Cite this

@article{5599ce5a5a804e98b208d3437ff2edae,

title = "On Uniqueness of Meromorphic Solutions to Some Differential-Difference Equations",

abstract = "Abstract: In this paper, we prove the uniqueness of finite-order transcendental meromorphic solutions of differential-difference Painlev{\'e} III and V equations: (Formula presented.) and (Formula presented.) where, and are small functions of solution. We show that if the solution shares,, and CM with another meromorphic function, then. Moreover, for Painlev{\'e} V equation, if is replaced by, it is sufficient for and to share the values and CM. MSC2020 numbers:30D35.",

keywords = "Nevanlinna{\textquoteright}s theory, differential-difference equation, meromorphic function, uniqueness",

author = "Z. Sui and J. Zhang",

note = "Publisher Copyright: {\textcopyright} Allerton Press, Inc. 2026.",

year = "2026",

month = feb,

doi = "10.3103/S1068362325700232",

language = "英语",

volume = "61",

pages = "61--72",

journal = "Journal of Contemporary Mathematical Analysis",

issn = "1068-3623",

publisher = "Pleiades Publishing",

number = "1",

}

TY - JOUR

T1 - On Uniqueness of Meromorphic Solutions to Some Differential-Difference Equations

AU - Sui, Z.

AU - Zhang, J.

N1 - Publisher Copyright: © Allerton Press, Inc. 2026.

PY - 2026/2

Y1 - 2026/2

N2 - Abstract: In this paper, we prove the uniqueness of finite-order transcendental meromorphic solutions of differential-difference Painlevé III and V equations: (Formula presented.) and (Formula presented.) where, and are small functions of solution. We show that if the solution shares,, and CM with another meromorphic function, then. Moreover, for Painlevé V equation, if is replaced by, it is sufficient for and to share the values and CM. MSC2020 numbers:30D35.

AB - Abstract: In this paper, we prove the uniqueness of finite-order transcendental meromorphic solutions of differential-difference Painlevé III and V equations: (Formula presented.) and (Formula presented.) where, and are small functions of solution. We show that if the solution shares,, and CM with another meromorphic function, then. Moreover, for Painlevé V equation, if is replaced by, it is sufficient for and to share the values and CM. MSC2020 numbers:30D35.

KW - Nevanlinna’s theory

KW - differential-difference equation

KW - meromorphic function

KW - uniqueness

UR - https://www.scopus.com/pages/publications/105033976461

U2 - 10.3103/S1068362325700232

DO - 10.3103/S1068362325700232

M3 - 文章

AN - SCOPUS:105033976461

SN - 1068-3623

VL - 61

SP - 61

EP - 72

JO - Journal of Contemporary Mathematical Analysis

JF - Journal of Contemporary Mathematical Analysis

IS - 1

ER -

On Uniqueness of Meromorphic Solutions to Some Differential-Difference Equations

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this