An existence result for gradient-type systems with a nondifferentiable term on unbounded strips
type: Item
instance of: scholarly article
title: An existence result for gradient-type systems with a nondifferentiable term on unbounded strips
zbMATH Open document ID: 1129.35423
author: Alexandru Kristály
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-03-08T00:00:00Z
review text: The author deals with the existence of nonzero solutions of the gradient-type system \[ -\Delta_p u= F_u(x,u,v)\quad\text{in }\Omega, \qquad -\Delta_q v= F_v(x,u,v)\quad\text{in }\Omega, \qquad u= v= 0\quad\text{on }\partial\Omega, \] where \(\Omega\) is a strip-like domains of the form \(\Omega= \omega\times\mathbb R^{N-m}\) with \(\omega\subset\mathbb{R}^m\) \((m\geq 1)\) is an open bounded set, \(N-m\geq 2\). Here \(F\in C^1(\Omega\times \mathbb R^2, \mathbb R)\), \(1< p\), \(q< N\) with \(F_u\) is the partial derivative of \(F\) with respect to \(u\) (similarly for \(F_v\)) and \(\Delta_\alpha u:= \text{div}(|\nabla u|^{\alpha-2}\nabla u)\), \(\alpha\in \{p,q\}\). To this end, the author uses a nonsmooth version of the mountain pass theorem which involves the Cerami condition and principle of symmetric criticality for locally Lipschitz functions.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J85
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35R70
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 2141776
zbMATH Keywords: Quasilinear elliptic systems
zbMATH Keywords: Strip-like domain
zbMATH Keywords: locally Lipschitz functions
zbMATH Keywords: Principle of symmetric criticality
zbMATH Keywords: Nonsmooth Cerami condition
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.06.026
OpenAlex ID: W2165537344
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DOI: 10.1016/J.JMAA.2004.06.026
description: scientific article; zbMATH DE number 2141776