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

被引：6

作者：

Du, Yunfei ^{[1
]}

Gao, Zongsheng ^{[1
]}

Zhang, Jilong ^{[1
]}

Zhao, Ming ^{[2
]}

机构：

[1] Beihang Univ, LMIB Sch Math & Syst Sci, Beijing, Peoples R China

[2] China Univ Geosci Beijing, Sch Sci, Beijing, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2018年

基金：

中国国家自然科学基金;

关键词：

Painleve equations; q-Difference; Meromorphic solution; INTEGRABILITY;

D O I：

10.1186/s13660-018-1790-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页数：13

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