Existence of blowup solutions for nonlinear problems with a gradient term
type: Item
instance of: scholarly article
title: Existence of blowup solutions for nonlinear problems with a gradient term
zbMATH Open document ID: 1141.35026
DOI: 10.1155/IJMMS/2006/80605
author: Faten Toumi
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2007-06-14T00:00:00Z
full work available at URL: https://eudml.org/doc/54349
review text: Summary: We prove the existence of positive explosive solutions for the equation \[ Au+\lambda(|x|)|\nabla u(x)|=\varphi(x, u(x)) \] in the whole space \(\mathbb{R}^N\) \((N\geq 3)\), where \(\lambda: [0,\infty)\to [0,\infty)\) is a continuous function and \(\varphi:\mathbb{R}^N\times[0, \infty)\to [0,\infty)\) is required to satisfy some particular hypotheses. More precisely, we give a necessary and sufficient condition for the existence of a positive solution that blows up at infinity.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 5164275
zbMATH Keywords: semilinear elliptic problems
zbMATH Keywords: gradient term
zbMATH Keywords: blowup solutions
zbMATH Keywords: existence
MaRDI profile type: Publication
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OpenAlex ID: W2086381253
description: scientific article; zbMATH DE number 5164275