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 $\mathbb R^N$, $0\leq a\in L^\infty (\Omega )$ and $g$ is a nonnegative continuous function on $(0,+\infty)$ which may have a singularity at zero.