Timeline for Existence of solutions to $\lambda u-\frac{1}{(1+(u')^2)^2} \, \Delta u = f$
Current License: CC BY-SA 3.0
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| when toggle format | what | by | license | comment | |
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| Dec 7, 2017 at 20:14 | comment | added | fedja | In other words, you want to know if there are stationary points of $$ I(u)=\int_a^b\left[\lambda\frac {u^2}2+G(u')-F(x,u)\right]\,dx $$ where $G(t)=\int_0^t\frac{1}{(1+s^2)^2}\,ds$ and $F(x,t)$ is an antiderivative of $f(x,s)$ with respect to $s$. In what regime do you have trouble with the existence of both the maximizer and the minimizer? | |
| Dec 7, 2017 at 13:39 | comment | added | Michael Renardy | If f=f(u), why not multiply the equation by u' and integrate once? | |
| Dec 7, 2017 at 13:35 | review | First posts | |||
| Dec 7, 2017 at 13:42 | |||||
| Dec 7, 2017 at 13:30 | history | asked | Abbre | CC BY-SA 3.0 |