一类非线性复微分方程亚纯解的情况
Meromorphic Solutions of a Class of Nonlinear Complex Differential Equations
DOI: 10.12677/PM.2025.1511264, PDF,    科研立项经费支持
作者: 张阳意：珠海科技学院大数据学院，广东 珠海；郭惠媛*：五邑大学数学与计算科学学院，广东 江门
关键词: 值分布；亚纯函数；复微分方程；存在性唯一性；Theory of Value Distribution； Meromorphic Function Solution； Complex Differential Equations； Uniqueness and Existence
摘要: 本文旨在研究形如f(z)n+pd(f)=p1eα1z+p2eα2z+p3eα3z的复微分方程亚纯解的存在性问题及解的形式和性质，用f(z)nf′(z)替换原方程的f(z)n，推广了陈敏风和陈宗煊的结果，得到方程的亚纯解情况，并举例进行说明。
Abstract: The article explores the existence, form, and properties of meromorphic solutions to complex differential equations of the form f(z)n+pd(f)=p1eα1z+p2eα2z+p3eα3z. By replacing f(z)n in the original equation with f(z)nf′(z), the chapter extends the results of Minfeng Chen and Zongxuan Chen. It presents the conditions for the equation’s meromorphic solutions and provides examples for illustration.
文章引用：张阳意, 郭惠媛. 一类非线性复微分方程亚纯解的情况[J]. 理论数学, 2025, 15(11): 11-16. https://doi.org/10.12677/PM.2025.1511264

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