International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 9, Pages 80605, 11 p.
doi:10.1155/IJMMS/2006/80605

Existence of blowup solutions for nonlinear problems with a gradient term

Abstract

We prove the existence of positive explosive solutions for the equation Δu+λ(|x|)|∇u(x)|=ϕ(x,u(x)) in the whole space ℝN(N≥3), where λ:[0,∞)→[0,∞) is a continuous function and ϕ: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.