Self-similar Differential Equations
Classical Analysis and ODEs
2024-09-17 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2409.09943,
title = {Self-similar Differential Equations},
author = {Leon Q. Brin and Joe Fields},
journal= {arXiv preprint arXiv:2409.09943},
year = {2024}
}
Comments
15 pages, 3 figures