Asymptotic behavior of solutions to a perturbed \(p\)-Laplacian problem with Neumann condition
type: Item
instance of: scholarly article
title: Asymptotic behavior of solutions to a perturbed \(p\)-Laplacian problem with Neumann condition
zbMATH Open document ID: 1210.35051
author: Everaldo S. de Medeiros
author: Jianfu Yang
published in: Discrete and Continuous Dynamical Systems
publication date: 2005-06-21T00:00:00Z
review text: The main goal of this paper is to study the existence and asymptotic behaviour of positive solutions of the following perturbed quasilinear elliptic Neumann problem \[ -\varepsilon\Delta_p u+ |u|^{p-2} u= |u|^{q-2} u\quad\text{in }\Omega,\quad{\partial u\over\partial n}= 0\quad\text{on }\partial\Omega, \] where \(\Delta_p\) denotes the \(p\)-Laplacian operator, \(\Delta_p u= \text{div}(|\nabla u|^{p-2}\,\nabla u)\), \(1< p< q< p^*= {N_p\over N-p}\), \(1< p< N\), \(\varepsilon> 0\) is a parameter, \(\Omega\subset\mathbb{R}^N\) \((N\geq 3)\) is a bounded smooth domain and \(n\) is the outer unit normal to \(\partial\Omega\).
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 2177451
zbMATH Keywords: positive solution
zbMATH Keywords: quasilinear elliptic problem
zbMATH Keywords: Neumann problem
zbMATH Keywords: asymptotic behaviour
MaRDI profile type: Publication
full work available at URL: dcds.2005.12.595
OpenAlex ID: W2031339100
DOI: 10.3934/DCDS.2005.12.595
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description: scientific article; zbMATH DE number 2177451