An elementary proof of the existence and uniqueness of solutions to an initial value problem

Autor:	Castrillón, Luca Tanganelli
Rok vydání:	2024
Předmět:	Mathematics - Classical Analysis and ODEs 34A12
Druh dokumentu:	Working Paper
Popis:	In this note, we show a classical result on the local existence and uniqueness of a solution to an initial value problem subject to a Lipschitz condition. We use only elementary tools from mathematical analysis, without involving any integration. We proceed by showing that the Cauchy iterates converge on a dense subset of the interval and subsequently proving that the extension of this limit function to the whole interval is a solution to the Cauchy problem. Comment: 8 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.06149 Zobrazit plný text záznamu View this record from Arxiv