{"title":"Self-similar Differential Equations","authors":"Leon Q. Brin, Joe Fields","doi":"arxiv-2409.09943","DOIUrl":null,"url":null,"abstract":"Differential equations where the graph of some derivative of a function is\ncomposed of a finite number of similarity transformations of the graph of the\nfunction itself are defined. We call these self-similar differential equations\n(SSDEs) and prove existence and uniqueness of solution under certain\nconditions. While SSDEs are not ordinary differential equations, the technique\nfor demonstrating existence and uniqueness of SSDEs parallels that for ODEs.\nThis paper appears to be the first work on equations of this nature.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09943","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.