Positive solutions in semilinear critical problems for polyharmonic operators
type: Item
instance of: scholarly article
title: Positive solutions in semilinear critical problems for polyharmonic operators
zbMATH Open document ID: 1210.35064
author: Yuxin Ge
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2005-05-04T00:00:00Z
review text: The author deals with the semilinear polyharmonic problem \[ \begin{gathered} (-\Delta)^k u= |u|^{s-2} u+ f(x,u)\quad\text{in }\Omega,\\ u> 0\quad\text{in }\Omega,\\ u= (-\Delta)u=\cdots=(-\Delta)^{k-1}= 0\quad\text{on }\partial\Omega,\end{gathered}\tag{1} \] where \(k\in\mathbb{N}\) and \(\Omega\subset\mathbb{R}^N\) \((N\geq 2k+1)\) is a regular bounded domain in \(\mathbb{R}^N\); \(s= {2N\over N-2k}\). The author studies the existence of solutions to (1) for general bounded domains under appropriate assumptions minimizing on some infinite-dimensional Finsler manifold. Moreover, he studies a concentration phenomenon.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J35
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 2164963
zbMATH Keywords: polyharmonic operators
zbMATH Keywords: semilinear critical problems
zbMATH Keywords: topological methods
zbMATH Keywords: Finsler manifold
MaRDI profile type: Publication
full work available at URL: j.matpur.2004.10.002
OpenAlex ID: W2018936938
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DOI: 10.1016/J.MATPUR.2004.10.002
description: scientific article; zbMATH DE number 2164963