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International Journal of Mathematics and Mathematical Sciences
Volume 2006, Article ID 80605, 11 pages

Existence of blowup solutions for nonlinear problems with a gradient term

Département des Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, Tunis 2092, Tunisia

Received 29 July 2005; Revised 7 March 2006; Accepted 25 April 2006

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.


We prove the existence of positive explosive solutions for the equation Δu+λ(|x|)|u(x)|=ϕ(x,u(x)) in the whole space N(N3), where λ:[0,)[0,) is a continuous function and ϕ:N×[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.