Entire blow-up solutions of semilinear elliptic systems with quadratic gradient terms
type: Item
instance of: scholarly article
title: Entire blow-up solutions of semilinear elliptic systems with quadratic gradient terms
zbMATH Open document ID: 1257.35094
DOI: 10.1155/2012/697565
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: We study the existence of entire positive solutions for the semilinear elliptic system with quadratic gradient terms, \(\Delta u_i + |\nabla u_i|^2 = p_i(|x|)f_i(u_1, u_2, \dots, u_d)\) for \(i = 1, 2, \dots, d\) on \(\mathbb R^N, N \geq 3\) and \(d \in \{1, 2, 3, \dots\}\). We establish the conditions on \(p_i\) that ensure the existence of nonnegative radial solutions blowing up at infinity and also the conditions for bounded solutions on the entire space. The condition on \(f_i\) is simple and different to the Keller-Osserman condition.
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35B09
Mathematics Subject Classification ID: 35B08
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 6134147
Wikidata QID: Q58696602
author: Yong-Ju Yang
author: Xinguang Zhang
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/697565
OpenAlex ID: W2170249646
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description: scientific article; zbMATH DE number 6134147