Existence of zero-order meromorphic solutions of certain q-difference equations

Yunfei Du; Zongsheng Gao; Jilong Zhang; Ming Zhao

doi:10.1186/s13660-018-1790-z

Existence of zero-order meromorphic solutions of certain q-difference equations

Yunfei Du
, Zongsheng Gao
, Jilong Zhang
, Ming Zhao^*

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University
China University of Geosciences, Beijing

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

6 Scopus citations

Abstract

In this paper, we consider the q-difference equation (f(qz)+f(z))(f(z)+f(z/q))=R(z,f), where R(z, f) is rational in f and meromorphic in z. It shows that if the above equation assumes an admissible zero-order meromorphic solution f(z) , then either f(z) is a solution of a q-difference Riccati equation or the coefficients satisfy some conditions.

Original language	English
Article number	217
Journal	Journal of Inequalities and Applications
Volume	2018
DOIs	https://doi.org/10.1186/s13660-018-1790-z
State	Published - 2018

Keywords

Meromorphic solution
Painlevé equations
q-Difference

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10.1186/s13660-018-1790-z

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title = "Existence of zero-order meromorphic solutions of certain q-difference equations",

abstract = "In this paper, we consider the q-difference equation (f(qz)+f(z))(f(z)+f(z/q))=R(z,f), where R(z, f) is rational in f and meromorphic in z. It shows that if the above equation assumes an admissible zero-order meromorphic solution f(z) , then either f(z) is a solution of a q-difference Riccati equation or the coefficients satisfy some conditions.",

keywords = "Meromorphic solution, Painlev{\'e} equations, q-Difference",

author = "Yunfei Du and Zongsheng Gao and Jilong Zhang and Ming Zhao",

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year = "2018",

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AU - Du, Yunfei

AU - Gao, Zongsheng

AU - Zhang, Jilong

AU - Zhao, Ming

PY - 2018

Y1 - 2018

N2 - In this paper, we consider the q-difference equation (f(qz)+f(z))(f(z)+f(z/q))=R(z,f), where R(z, f) is rational in f and meromorphic in z. It shows that if the above equation assumes an admissible zero-order meromorphic solution f(z) , then either f(z) is a solution of a q-difference Riccati equation or the coefficients satisfy some conditions.

AB - In this paper, we consider the q-difference equation (f(qz)+f(z))(f(z)+f(z/q))=R(z,f), where R(z, f) is rational in f and meromorphic in z. It shows that if the above equation assumes an admissible zero-order meromorphic solution f(z) , then either f(z) is a solution of a q-difference Riccati equation or the coefficients satisfy some conditions.

KW - Meromorphic solution

KW - Painlevé equations

KW - q-Difference

UR - https://www.scopus.com/pages/publications/85051777239

U2 - 10.1186/s13660-018-1790-z

DO - 10.1186/s13660-018-1790-z

M3 - 文章

AN - SCOPUS:85051777239

SN - 1025-5834

VL - 2018

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

M1 - 217

ER -

Existence of zero-order meromorphic solutions of certain q-difference equations

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Keywords

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