一类阿贝尔方程组的求解问题  

Solutions of a Class of Abel Equations

作　　者：袁江青 YUAN Jiangqing(School of Mathematical Sciences,Chongqing Normal University,Chongqing,401331,P.R.China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《数学进展》2024年第3期653-661,共9页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11671061)。

摘　　要：本文考虑联立阿贝尔(Abel)方程■的连续解,首先需要解决的是2个阿贝尔方程组成的联立方程,在求解过程中需要先获得单个阿贝尔方程的一个单调连续解,并通过此连续解构造新的2个阿贝尔方程组成的联立方程,然后在复平面上构造一个同胚映射进而求得一个连续解,2个阿贝尔方程组成的联立方程的连续解由这两个解复合得出.在2个阿贝尔方程组成的联立方程基础之上,进而求得n个阿贝尔方程组成的联立方程的连续解,得出此类联立方程的解是单调且连续的.In this paper,considering the continuous solution of the simultaneous Abel equation■the first thing to be solved is the simultaneous equation composed of two Abel equations.In the process of solving,a monotone continuous solution of a single Abel equation should be obtained first,and a new simultaneous equation composed of two Abel equations should be constructed from this continuous solution.Then a homeomorphic mapping is constructed on the complex plane to obtain a continuous solution.The continuous solution of the simultaneous equation composed of two Abel equations is obtained from the composition of these two solutions.On the basis of the simultaneous equation composed of two Abel equations,the continuous solution of the simultaneous equation composed of n Abel equations is obtained,which is monotonous and continuous.

关 键 词：阿贝尔方程 单调 连续 联立方程 同胚映射 

分 类 号：O175.7[理学—数学] O174.23[理学—基础数学]