• 论文 •

### JULIA LIMITING DIRECTIONS OF ENTIRE SOLUTIONS OF COMPLEX DIFFERENTIAL EQUATIONS

1. 1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;
2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
• 收稿日期:2020-05-04 出版日期:2021-08-25 发布日期:2021-09-01
• 通讯作者: Xiao YAO E-mail:yaoxiao@nankai.edu.cn
• 作者简介:Jun WANG,E-mail:majwang@fudan.edu.cn;Xiao YAO,E-mail:yaoxiao@nankai.edu.cn;Chengchun ZHANG,E-mail:18210180014@fudan.edu.cn
• 基金资助:
This work was supported by the National Natural Science Foundation of China (11771090, 11901311) and Natural Sciences Foundation of Shanghai (17ZR1402900).

### JULIA LIMITING DIRECTIONS OF ENTIRE SOLUTIONS OF COMPLEX DIFFERENTIAL EQUATIONS

Jun WANG1, Xiao YAO2, Chengchun ZHANG2

1. 1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;
2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
• Received:2020-05-04 Online:2021-08-25 Published:2021-09-01
• Contact: Xiao YAO E-mail:yaoxiao@nankai.edu.cn
• Supported by:
This work was supported by the National Natural Science Foundation of China (11771090, 11901311) and Natural Sciences Foundation of Shanghai (17ZR1402900).

Abstract: For entire or meromorphic function $f$, a value $\theta\in[0,2\pi)$ is called a Julia limiting direction if there is an unbounded sequence $\{z_n\}$ in the Julia set satisfying $\lim\limits_{n\rightarrow\infty}\arg z_n=\theta.$ Our main result is on the entire solution $f$ of $P(z,f)+F(z)f^s=0$, where $P(z,f)$ is a differential polynomial of $f$ with entire coefficients of growth smaller than that of the entire transcendental $F$, with the integer $s$ being no more than the minimum degree of all differential monomials in $P(z,f)$. We observe that Julia limiting directions of $f$ partly come from the directions in which $F$ grows quickly.

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