Self-similar Differential Equations

Leon Q. Brin, Joe Fields
{"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.
自相似微分方程
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信