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

Journal of Inequalities and Applications

Jilong Zhang¹  Yunfei Du¹  Zongsheng Gao¹  Ming Zhao² 

[1] LMIB-School of Mathematics and Systems Science, Beihang University;School of Science, China University of Geosciences (Beijing);

关键词: Painlevé equations;    q-Difference;    Meromorphic solution;   

DOI  :  10.1186/s13660-018-1790-z

来源: DOAJ

【 摘 要 】

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

【 授权许可】

Unknown