Hello, I know a theorem that say that if ##F : \mathbb{R} \times \Omega \rightarrow E## is continuous and local lispchitziann in is seconde set value(where ##\Omega## is an open of a Banach space E.). we have that the maximum solution ##(\phi, J)##(where J is an open intervall and ##\phi : J \rightarrow \Omega## is ##C^{1}## .). of ##\phi'(t) = F(t, \phi(t))## diverge if ##sup(J) < + \infty##(##lim_{t \rightarrow sup(J)} \phi(t) = +\infty##.).(adsbygoogle = window.adsbygoogle || []).push({});

Is there the same results if F is just continuos please?

Thank you in advance and have a nice aftrenoon.

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# I Maximal solution theorem

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