Quasilinear equations with natural growth

Abstract

We study the existence of positive solution $w\in H_0^1(\Omega )$ of the quasilinear equation $-\Delta w+g(w)|\nabla w{|}^2=a(x)$, $x\in \Omega$, where $\Omega$ is a bounded domain in ${\mathbb{R}}^N$, $0\le a\in L^{\infty }(\Omega )$ and $g$ is a nonnegative continuous function on $(0,+\infty )$ which may have a singularity at zero.