自相似微分方程

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-09-16 DOI:arxiv-2409.09943

Leon Q. Brin, Joe Fields

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引用次数: 0

摘要

我们定义了函数的某些导数的图形由函数本身图形的有限个相似变换组成的微分方程。我们称这些方程为自相似微分方程（SSDE），并证明在特定条件下解的存在性和唯一性。虽然 SSDE 并非常微分方程，但证明 SSDE 存在性和唯一性的技术与常微分方程类似。

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Self-similar Differential Equations

Differential equations where the graph of some derivative of a function is composed of a finite number of similarity transformations of the graph of the function itself are defined. We call these self-similar differential equations (SSDEs) and prove existence and uniqueness of solution under certain conditions. While SSDEs are not ordinary differential equations, the technique for demonstrating existence and uniqueness of SSDEs parallels that for ODEs. This paper appears to be the first work on equations of this nature.

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arXiv - MATH - Classical Analysis and ODEs

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