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Community Bot
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I think it is worth mentioning that although it is true that Lipschitz continuity guarantees unique solutions, there is a weaker regularity condition for $f$ which also gives uniqueness. The buzzword is "Osgood condition" and the theorem is given in Andrey Rekalo's answer to this MO questionthis MO question on "Existence/Uniqueness of solutions to quasi-Lipschitz ODEs".

I think it is worth mentioning that although it is true that Lipschitz continuity guarantees unique solutions, there is a weaker regularity condition for $f$ which also gives uniqueness. The buzzword is "Osgood condition" and the theorem is given in Andrey Rekalo's answer to this MO question on "Existence/Uniqueness of solutions to quasi-Lipschitz ODEs".

I think it is worth mentioning that although it is true that Lipschitz continuity guarantees unique solutions, there is a weaker regularity condition for $f$ which also gives uniqueness. The buzzword is "Osgood condition" and the theorem is given in Andrey Rekalo's answer to this MO question on "Existence/Uniqueness of solutions to quasi-Lipschitz ODEs".

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Dirk
Dirk
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I think it is worth mentioning that although it is true that Lipschitz continuity guarantees unique solutions, there is a weaker regularity condition for $f$ which also gives uniqueness. The buzzword is "Osgood condition" and the theorem is given in Andrey Rekalo's answer to this MO question on "Existence/Uniqueness of solutions to quasi-Lipschitz ODEs".