Some remarks on a system of quasilinear elliptic equations
type: Item
instance of: scholarly article
title: Some remarks on a system of quasilinear elliptic equations
zbMATH Open document ID: 1011.35050
author: Djairo G. de Figueiredo
author: Lucio Boccardo
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2002-12-01T00:00:00Z
review text: The present paper deals with the functional \[ \Phi(u,v)= {1\over p} \int_\Omega |\nabla u|^p+ {1\over q}\int_\Omega|\nabla v|^q-\int_\Omega F(x,u,v)\,dx, \tag{1} \] where \(p\) and \(q\) are real numbers larger than \(1,\Omega\) is some bounded domain in \(\mathbb R^N\), \(u\) and \(v\) are real-valued functions defined in \(\overline\Omega\) and belonging to appropriate spaces of functions and \(F\) is a potential. The goal of the authors is to study the geometry of this functional viewing to determining its critical points.
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 58E30
zbMATH DE Number: 1836993
zbMATH Keywords: functional
zbMATH Keywords: critical point
zbMATH Keywords: quasilinear elliptic equations
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s00030-002-8130-0
OpenAlex ID: W4253784537
DOI: 10.1007/S00030-002-8130-0
description: scientific article; zbMATH DE number 1836993