Existence of global solutions of elliptic systems
type: Item
instance of: scholarly article
title: Existence of global solutions of elliptic systems
zbMATH Open document ID: 1160.35403
author: Roberta Filippucci
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-06T00:00:00Z
review text: The author deals with the existence of entire solutions of elliptic systems \[ \begin{aligned} &\text{div} (| u|^\gamma |\nabla u|^{m-2} \nabla u)- \tfrac \gamma m | u|^{\gamma-2} u|\nabla u|^m=| u|^{p-2}u,\\ &u:\mathbb{R}^n\to \mathbb{R}^d, \quad\text{with }m>1, \;\gamma\in \mathbb{R},\;p>1. \end{aligned} \tag{1} \] The author proves that, if \(\gamma\geq p-m\), then (1) admits a one-parameter family of nontrivial entire radial solutions, \(u= u(| x|)\), such that \(\lim_{| x|\to\infty}| u(| x|)|= \infty\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J45
zbMATH DE Number: 2082171
zbMATH Keywords: elliptic systems
zbMATH Keywords: entire solution
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.01.027
OpenAlex ID: W2141768297
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DOI: 10.1016/J.JMAA.2004.01.027
description: scientific article; zbMATH DE number 2082171