Optimal version of the Picard-Lindelöf theorem
Consider the differential equation y 0 = F(x, y). We determine the weakest possible upper bound on |F(x, y) − F(x, z)| which guarantees that this equation has for all initial values a unique solution, which exists globally.
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2021
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenletek - közönséges, Picard-Lindelöf tétel |
| doi: | 10.14232/ejqtde.2021.1.39 |
| Online Access: | http://acta.bibl.u-szeged.hu/73691 |
| Tartalmi kivonat: | Consider the differential equation y 0 = F(x, y). We determine the weakest possible upper bound on |F(x, y) − F(x, z)| which guarantees that this equation has for all initial values a unique solution, which exists globally. |
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| Terjedelem/Fizikai jellemzők: | 8 |
| ISSN: | 1417-3875 |