Existence of blowup solutions for nonlinear problems with a gradient term

Faten Toumi
2006 International Journal of Mathematics and Mathematical Sciences  
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.
doi:10.1155/ijmms/2006/80605 fatcat:72zfu46f6jh7td6btrovqczctu