On a nonlinear fourth-order elliptic equation involving the critical Sobolev exponent
type: Item
instance of: scholarly article
title: On a nonlinear fourth-order elliptic equation involving the critical Sobolev exponent
zbMATH Open document ID: 1022.35012
DOI: 10.1016/S0362-546X(02)00273-0
author: François Bille Ebobisse
author: Mohameden Ould Ahmedou
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: The authors look for solutions to the problem \[ \Delta^{2} u(x)=u^{(n+4)/(n-4)}(x),\;x\in\Omega,\qquad u(x)>0,\;x\in\Omega,\qquad u(x)=\Delta u(x)=0, \;x\in\partial\Omega,\tag{P} \] where \(\Omega\) is a bounded smooth domain of \({\mathbb R}^{n}\) and \(n\geq 5\). Denote by \(H_{k}(\Omega, Z_{2})\) the homology of dimension \(k\) with coefficient in \(\mathbb{Z}_{2}\), then the authors prove the following theorem: Theorem. If \(H_{k}(\Omega, \mathbb{Z}_{2})\not=\emptyset\) for some \(k\in {\mathbb N}\), then problem (P) has a solution. This solution is characterized to be of higher energy and higher index. The methods used in proving that the result rely on topological arguments was already introduced in [\textit{A. Bahri} and \textit{J.-M. Coron}, Commun. Pures Appl. Math. 253-294 (1988; Zbl 0649.35033)].
reviewed by: Piero Montecchiari
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35B38
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35A15
zbMATH DE Number: 1880110
zbMATH Keywords: critical points at infinity
zbMATH Keywords: critical Sobolev exponent
zbMATH Keywords: higher order elliptic PDE
MaRDI profile type: Publication
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full work available at URL: s0362-546x(02)00273-0
OpenAlex ID: W2066935641
description: scientific article; zbMATH DE number 1880110