We prove the existence of positive explosive solutions for the equationΔu+λ(|x|)|∇u(x)|=ϕ(x,u(x))in the whole spaceℝN(N≥3), whereλ:[0,∞)→[0,∞)is a continuous function andϕ:ℝN×[0,∞)→[0,∞)is required to satisfy some hypotheses detailed below. More precisely, we will give a necessary and sufficient condition for the existence of a positive solution that blows up at infinity.