Existence of blowup solutions for nonlinear problems with a gradient term

Faten Toumi

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-11

Abstract:

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

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:080605

DOI: 10.1155/IJMMS/2006/80605

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