Quasilinear elliptic systems with critical Sobolev exponents in \(\mathbb {R}^N\)
type: Item
instance of: scholarly article
title: Quasilinear elliptic systems with critical Sobolev exponents in \(\mathbb {R}^N\)
zbMATH Open document ID: 1118.35023
author: Ali Djellit
author: Saadia Tas
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-04-13T00:00:00Z
review text: The paper deals with a quasilinear system involving the \(p\)-Laplacian on \(\mathbb R^N\), the critical Sobolev exponent and a parameter \(\lambda>0\). The existence of a nontrivial weak solution provided \(\lambda\) is sufficiently small is shown. The main technical tools are the verification of the Palais-Smale condition at levels in a specific range and application of the mountain pass theorem.
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 5142208
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: weak solution
zbMATH Keywords: Palais-Smale condition
zbMATH Keywords: mountain pass theorem
zbMATH Keywords: concentration-compactness principle
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
full work available at URL: j.na.2006.02.005
OpenAlex ID: W2032394104
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DOI: 10.1016/J.NA.2006.02.005
description: scientific article; zbMATH DE number 5142208