Quasilinear equations with natural growth (Q951991)

Summary: 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.