Existence of blowup solutions for nonlinear problems with a gradient term

Toumi, Faten

doi:https://doi.org/10.1155/IJMMS/2006/80605

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 080605 | https://doi.org/10.1155/IJMMS/2006/80605

Existence of blowup solutions for nonlinear problems with a gradient term

Faten Toumi¹

Received29 Jul 2005

Revised07 Mar 2006

Accepted25 Apr 2006

Published31 Jul 2006

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.

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Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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