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Timeline for fixed point arguments in PDE

Current License: CC BY-SA 3.0

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Jul 24 at 21:26 comment added Otis Chodosh @TarekAcila, You need a uniform $M$ that works for all $(x,\sigma)$.
Jul 24 at 17:24 comment added Tarek Acila I have a question in regard the bound in the Leray-Schauder theorem. If we are taking $(x, \sigma) \in \mathscr{B} \times[0,1]$ why (probably how) do we need to prove that $ \Vert x \Vert_\mathscr{B} \leq M.$ Does taking $x$ from $\mathscr{B}$ not already imply that $ \Vert x \Vert_\mathscr{B} $ is bounded?
Dec 3, 2012 at 15:10 comment added S. Carnahan In a now-deleted answer, Craig says: Thank you very much for the detailed example. Actually I very much enjoy this example.
Nov 24, 2012 at 16:44 history answered Otis Chodosh CC BY-SA 3.0