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Jul 19, 2022 at 9:46 comment added Danilo Gregorin Afonso @CarloBeenakker thank you. Unfortunately this is too restrictive: $f(r) = g'(u(r))$, where $u$ is the radial solution of $- \Delta u = g(u)$ in the unit ball (with Dirichlet condition). Maybe some specific nonlinearity $g$ would give some good information?
Jul 18, 2022 at 19:42 comment added Carlo Beenakker if $f(r)=r^p$ the solution is still a Bessel function, with argument $r^{1+p/2}$.
Jul 18, 2022 at 12:30 history asked Danilo Gregorin Afonso CC BY-SA 4.0