On the Non-existence of Meromorphic Solutions of Certain Types of Non-linear Differential Equations

被引：0
作者：
Huifang Liu
Zhiqiang Mao
机构：
[1] Jiangxi Normal University,College of Mathematics and Information Science
[2] Jiangxi Science and Technology Normal University,School of Mathematics and Computer
来源：
Computational Methods and Function Theory | 2019年 / 19卷
关键词：
Nevanlinna theory; Differential polynomial; Non-linear differential equation; Meromorphic solution; 30D35; 34M05;
D O I：
暂无
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学科分类号：
摘要：
In this paper, we study meromorphic solutions of non-linear differential equations of the form fn+Pd(f)=p1eα1(z)+p2eα2(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f^n+P_d(f)=p_1e^{\alpha _1(z)}+p_2e^{\alpha _2(z)}$$\end{document}, where α1,α2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _1,\alpha _2$$\end{document} are polynomials of degree k(≥1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k(\ge 1)$$\end{document}, p1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_1$$\end{document}, p2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_2$$\end{document} are small meromorphic functions of ezk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e^{z^k}$$\end{document}, Pd(f)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_\mathrm{d}(f)$$\end{document} is a differential polynomial in f of degree d with small meromorphic functions of f as its coefficients. Some sufficient conditions on the non-existence of meromorphic solutions of such equations are provided. Our results complement some previous results.
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页码：383 / 399
页数：16
相关论文
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