Quasilinear equations with natural growth

Abstract

We study the existence of positive solution w ∈ H01(Ω) of the quasilinear equation -Δw + g(w)|∇w|2 = a(x), x ∈ Ω, where Ω is a bounded domain in ℝN, 0 ≤ a ∈ L∞ (Ω) and g is a nonnegative continuous function on (0, +∞) which may have a singularity at zero.