Existence of blowup solutions for nonlinear problems with a gradient term

摘要

We prove the existence of positive explosive solutions for theequationΔu+λ(|x|)|?u(x)|=?(x,u(x))in the whole space?N(N≥3), whereλ:[0,∞)→[0,∞)is a continuous function and?:?N×[0,∞)→[0,∞)isrequired to satisfy some hypotheses detailed below. Moreprecisely, we will give a necessary and sufficient condition forthe existence of a positive solution that blows up at infinity.