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^*

^*此作品的通讯作者

数学科学学院

Beihang University
China University of Geosciences, Beijing

科研成果: 期刊稿件 › 文章 › 同行评审

6 引用（Scopus）

摘要

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.

源语言	英语
文章编号	217
期刊	Journal of Inequalities and Applications
卷	2018
DOI	https://doi.org/10.1186/s13660-018-1790-z
出版状态	已出版 - 2018

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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.",

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AU - Du, Yunfei

AU - Gao, Zongsheng

AU - Zhang, Jilong

AU - Zhao, Ming

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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

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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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