Beyond Peano's theorem: a variational look at discontinuous ODE systems
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910687709626368 |
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| author | Pedregal, Pablo |
| author_facet | Pedregal, Pablo |
| contents | We propose a framework to define solutions of ODE systems under a novel condition that goes well beyond the usual continuity condition required in the classical theory of ODEs (Peano's or Picard's theorems). We illustrate our results with some simple but enlightening examples, including some facts about Sobolev fields, and mention some relevant questions to proceed with this analysis further. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04536 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Beyond Peano's theorem: a variational look at discontinuous ODE systems Pedregal, Pablo Classical Analysis and ODEs 34A36 We propose a framework to define solutions of ODE systems under a novel condition that goes well beyond the usual continuity condition required in the classical theory of ODEs (Peano's or Picard's theorems). We illustrate our results with some simple but enlightening examples, including some facts about Sobolev fields, and mention some relevant questions to proceed with this analysis further. |
| title | Beyond Peano's theorem: a variational look at discontinuous ODE systems |
| topic | Classical Analysis and ODEs 34A36 |
| url | https://arxiv.org/abs/2411.04536 |