A remark on the linearized stability of positive solutions for systems involving the \(p\)-Laplacian
type: Item
instance of: scholarly article
title: A remark on the linearized stability of positive solutions for systems involving the \(p\)-Laplacian
zbMATH Open document ID: 1123.35014
author: Ghasem A. Afrouzi
author: S. H. Rasouli
published in: Positivity
publication date: 2007-06-07T00:00:00Z
review text: This paper is devoted to the stability properties of positive stationary solutions for nonlinear elliptic systems of the form \[ \begin{gathered} -\Delta_p u=\lambda f(u,v)\quad\text{in }\Omega,\\ -\Delta_pv=\lambda g(u,v)\quad\text{in }\Omega,\\ Bu= 0= Bv\quad\text{on }\partial\Omega,\end{gathered} \] where \(\Delta_p\) denotes the \(p\)-Laplacian, \(p> 2\), \(\Omega\) is a bounded domain in \(\mathbb R^d\) \((d> 1)\) with smooth boundary, \[ Bz(x):= \alpha h(x) z+(1- \alpha){\partial z\over\partial n} \] with \(\alpha\in [0,1]\) is a constant, \(h: \partial\Omega\to \mathbb{R}^+\) satisfying some natural assumptions, \(\lambda> 0\), \(f\), \(g\) are \(C^2\) function on \([0,\infty)\times [0,\infty)\).
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 5162440
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: elliptic system
zbMATH Keywords: linearized stability
MaRDI profile type: Publication
full work available at URL: s11117-006-2021-2
OpenAlex ID: W2034465248
cites work: Some remarks on a system of quasilinear elliptic equations
cites work: On positive weak solutions for a class of quasilinear elliptic systems
cites work: Existence of positive solutions for a nonvariational quasilinear elliptic system
cites work: Existence and uniqueness of positive solutions of semilinear elliptic systems
cites work: On some nonlinear elliptic systems
cites work: On a class of semilinear elliptic systems.
cites work: An existence result on positive solutions for a class of \(p\)-Laplacian systems.
cites work: Existence of coupled quasi-solutions of systems of nonlinear elliptic boundary value problems
cites work: Q5628581
cites work: Regularity for a more general class of quasilinear equations
DOI: 10.1007/S11117-006-2021-2
description: scientific article; zbMATH DE number 5162440