An elementary proof of the existence and uniqueness of solutions to an initial value problem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929586123571200 |
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| author | Castrillón, Luca Tanganelli |
| author_facet | Castrillón, Luca Tanganelli |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06149 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An elementary proof of the existence and uniqueness of solutions to an initial value problem Castrillón, Luca Tanganelli Classical Analysis and ODEs 34A12 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. |
| title | An elementary proof of the existence and uniqueness of solutions to an initial value problem |
| topic | Classical Analysis and ODEs 34A12 |
| url | https://arxiv.org/abs/2411.06149 |