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I Maximal solution theorem

  1. Aug 17, 2016 #1
    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##.).

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

    Thank you in advance and have a nice aftrenoon:oldbiggrin:.
     
  2. jcsd
  3. Aug 22, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
  4. Aug 23, 2016 #3
    Hello and thanks. In fact I recently knew that the local lipschitz condition is necessar for the uniqueness of a local solution to a diffential equation. I can give more if you want.
     
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