Meromorphic Solutions of Certain Types of Non-linear Differential Equations

被引：1
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 | 2020年 / 20卷
关键词：
Nevanlinna theory; Differential polynomial; Differential equation; Meromorphic solution; 34M05; 30D35;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let p1,p2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_1, p_2$$\end{document} and 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} be non-zero constants, and Pd(z,f)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_d(z, f)$$\end{document} be a differential polynomial in f of degree d. Li obtained the forms of meromorphic solutions with few poles of the non-linear differential equations fn+Pd(z,f)=p1eα1z+p2eα2z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f^n+P_d(z, f)=p_1e^{\alpha _1 z}+p_2e^{\alpha _2 z}$$\end{document} provided α1≠α2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha _1\ne \alpha _2$$\end{document} and d≤n-2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\le n-2$$\end{document}. In this paper, given d=n-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=n-1$$\end{document}, we find the forms of meromorphic solutions with few poles of the above equations under some restrictions on 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}. Some examples are given to illustrate our results.
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页码：319 / 332
页数：13
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