Solution to the iterative differential equation $-γg' = g^{-1}$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909306545242112 |
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| author | Miyamoto, Roland |
| author_facet | Miyamoto, Roland |
| contents | Using a Picard-like operator $T$, we prove that the iterative differential equation $-γg' = g^{-1}$ with parameter $γ>0$ has a solution $g=h\colon[0,1]\to[0,1]$ for only one value $γ=κ\approx0.278877$, and that this solution $h$ is unique. As an even stronger result, we exhibit $h$ as the global limit of the operator $T$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solution to the iterative differential equation $-γg' = g^{-1}$ Miyamoto, Roland Classical Analysis and ODEs Dynamical Systems 34K43, 47H10, 47J25, 33E30 Using a Picard-like operator $T$, we prove that the iterative differential equation $-γg' = g^{-1}$ with parameter $γ>0$ has a solution $g=h\colon[0,1]\to[0,1]$ for only one value $γ=κ\approx0.278877$, and that this solution $h$ is unique. As an even stronger result, we exhibit $h$ as the global limit of the operator $T$. |
| title | Solution to the iterative differential equation $-γg' = g^{-1}$ |
| topic | Classical Analysis and ODEs Dynamical Systems 34K43, 47H10, 47J25, 33E30 |
| url | https://arxiv.org/abs/2404.11455 |