Let $\Omega$ be a bounded open set in $\mathbb{R}^n$ and $u\in H^1(\Omega)\cap L^{\infty}(\Omega)$ be the weak subsolution of the following nonlinear and heterogeneous elliptic equation: $-\nabla\cdot(|\nabla u|^{p-2}\nabla u)+c(x)|u|^{p-2}u=f$ where $0\le c(x)\le M$ and $f\in L^\infty(\Omega)$. That is, for every $\phi\in H^1(\Omega)\cap L^{\infty}(\Omega)$, $\int_\Omega|\nabla u|^{p-2}\nabla u\cdot\nabla\phi+c(x)|u|^{p-2}u\phi\,dx\le\int_\Omega f\phi\,dx$
Show that there exists a constant $R_0=R_0(M)>0$, such that for every $0
I think this can be done by a generalized version of Moser iteration, extended from linear case to nonlinear one. Can anyone give some clues or references? Thank you~