Timeline for leray schauder fixed point and schauder fixed point
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5 events
| when toggle format | what | by | license | comment | |
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| Jan 21, 2022 at 17:10 | vote | accept | mnmn1993 | ||
| Apr 28, 2016 at 16:04 | comment | added | Willie Wong | Perhaps it would be easier if you think of the condition in Leray-Schauder as "... there exists some constant $M$ such that if $\|u\| > M$ then $\sigma T(u) \neq u$ for any $\sigma \in [0,1]$." What you are doing is not finding fixed points, but putting constraints on what could potentially be fixed points. | |
| Apr 28, 2016 at 16:03 | comment | added | Willie Wong | @mnmn1993: Of course "finding the fixed point of $\sigma T$" is similar to finding those of $T$. But the key thing that you miss is that you can prove the statement "If $u$ solves $\sigma T(u) = u$ then $\|u\| \leq 1$" without knowing that such $u$ actually exist! In other words, in using Leray-Schauder you are never asked to find the fixed points of $\sigma T$. | |
| Apr 28, 2016 at 15:41 | comment | added | mnmn1993 | Thank you so much! It is so clear . But for a PDE question , if i choose to apply leray schauder theorem ,can i say finding the fixed of $\sigma T(u)=u$ is very similar to $T(u)=u$ ? | |
| Apr 28, 2016 at 15:15 | history | answered | Willie Wong | CC BY-SA 3.0 |