某类非线性微分方程的亚纯解  

Meromorphic Solutions of Certain Nonlinear Differential Equations

作　　者：陈敏风 陈宗煊[2] Min Feng CHEN;Zong Xuan CHEN(School of Mathematics and Statistics,Guangdong University of Foreign Studies,Guangzhou 510006,P.R.China;School of Mathematical Sciences,South China Normal University,Guangzhou510631,P.R.China)

机构地区：[1]广东外语外贸大学数学与统计学院,广州510006 [2]华南师范大学数学科学学院,广州510631

出　　处：《数学学报（中文版）》2023年第6期1205-1220,共16页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12001117);广州市科技计划项目(202102020438);广东省区域联合基金-青年基金资助项目(2021A1515110654)。

摘　　要：在一定条件下,本文给出了非线性微分方程f^(n)(z)+Pd(z,f)=p1e^(a1z)+p2e^(a2z)+p3e^(a3z)亚纯解的表达式,其中n≥3为正整数,p_(d)(z,f)≠0为关于f的微分多项式,次数d≤n-1,系数为f的小函数,p_(j)(j=1,2,3)为非零常数,α_(j)(j=1,2,3)为互异的非零常数.而且,给出了相应的例子辅以说明.The main purpose of this paper is to give the expressions of meromorphic solutions of the following non-linear differential equation f^(n)(z)+Pd(z,f)=p1e^(a1z)+p2e^(a2z)+p3e^(a3z)under certain conditions,where n≥3 is an integer,P_(d)(z,f)≠0 is a differential polynomial in f of degree d≤n-1 with small function coefficients,p_(j)(j=1,2,3)are non-zero constants,α_(j)(j=1,2,3)are three distinct non-zero constants.Moreover,some examples are given to illustrate our results.

关 键 词：NEVANLINNA理论 非线性微分方程 亚纯解 

分 类 号：O174.52[理学—数学]