A Note on an Iterative Equation Related to Painlevé Equations

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2025-10-06 DOI:10.1007/s10255-024-1030-x

Wei Cheng

引用次数: 0

Abstract

In this paper, we explore the existence of analytic solutions for an iterative functional equation of the form

$$g(g(x))+x=f(g(x))$$

that originates from Painlevé equations. By an invertible transformation, we study the analytic solutions of an auxiliary equation under three different cases, and obtain the invertible analytic solutions for the original equation.

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关于疼痛水平方程的一个迭代方程的注记

本文研究了一类迭代泛函方程$$g(g(x))+x=f(g(x))$$解析解的存在性，该方程起源于painlev方程。通过可逆变换，研究了三种不同情况下辅助方程的解析解，得到了原方程的可逆解析解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Mathematicae Applicatae Sinica, English Series 数学-应用数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.