what should be the range of $u$ satisfying following equation. Let us consider that $u\in C^2(\Omega)\cap C^0(\Omega)$ and satisfying the following equation . 
$\Delta u=u^3-u , x\in\Omega$ and 
$u=0 $   in  $\partial \Omega$
$\Omega \subset \mathbb R^n$ and bounded . 
I need hints to find out what possible value $u$ can take ? 
Thank you for ur hints in advance . 

We must of course assume $u$ is continuous on the closure of $\Omega$.
Since this is bounded and $u = 0$ on $\partial \Omega$, if $u > 0$ somewhere it must achieve a maximum in $\Omega$.  Now $u$ is subharmonic on any part of the domain where $u > 1$, so the maximum principle says ...
