On the stationary solutions of generalized reaction diffusion equations with \(p\)\& \(q\)-Laplacian
type: Item
instance of: scholarly article
title: On the stationary solutions of generalized reaction diffusion equations with \(p\)\& \(q\)-Laplacian
zbMATH Open document ID: 1210.35090
published in: Communications on Pure and Applied Analysis
publication date: 2005-06-21T00:00:00Z
review text: The authors deal with the study of the existence and non-existence results for solutions to the following stationary nonlinear equation \[ -\text{div}([|\nabla_x u|^{p-2}+ |\nabla_x u|^{q-2}]\,\nabla_x u)+ q(x)|u|^{p-2} u+ w(x)|u|^{q-2}_x= \lambda f(x)|u|^{q-2} u\tag{1} \] considered in a bounded domain \(\Omega\subset\mathbb{R}^d\), \(d\geq 1\), subject to the Dirichlet boundary condition \(u=0\) on \(\partial\Omega\). The authors study problem (1) with respect to the real parameter \(\lambda\). They introduce a new type variational principles corresponding to this family of equations.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 2177439
zbMATH Keywords: stationary solution
zbMATH Keywords: \(p\)- and \(q\)-Laplacian
zbMATH Keywords: existence and non-existence result
author: Laurence Cherfils
author: Ya. Sh. Il'yasov
MaRDI profile type: Publication
full work available at URL: cpaa.2005.4.9
OpenAlex ID: W1990225435
DOI: 10.3934/CPAA.2005.4.9
description: scientific article; zbMATH DE number 2177439