On an elliptic problem with critical nonlinearity in expanding annuli
type: Item
instance of: scholarly article
title: On an elliptic problem with critical nonlinearity in expanding annuli
zbMATH Open document ID: 0954.35068
author: Khalil O. El Mehdi
author: Mohameden Ould Ahmedou
published in: Journal of Functional Analysis
publication date: 2001-02-05T00:00:00Z
review text: This is a continuation of papers by \textit{M. O. Ahmedou} and \textit{K. O. El Mehdi} [Computation of the difference of topology at infinity for Yamabe-type problems on annuli-domains. I, II. Duke Math. J. 94, No. 2, 215-229, 231-255 (1998; Zbl 0966.35043)] in computing the difference of the topology between the level sets caused by the critical points at infinity. The program is initiated by A. Bahri and J. M. Coron in the study of the Kazdan Warner problem in Riemannian geometry. In this paper, the authors study the critical nonlinear elliptic problem on the expanding annuli \(A_\varepsilon= \{x\in \mathbb{R}^n\mid\varepsilon<|x|<{1\over \varepsilon}\}\), and make the above computation for \(\varepsilon\to 0\).
reviewed by: Kung Ching Chang
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 1278793
zbMATH Keywords: critical point at infinity
zbMATH Keywords: lack of compactness
zbMATH Keywords: critical nonlinearity
MaRDI profile type: Publication
full work available at URL: jfan.1998.3340
OpenAlex ID: W1984031237
cites work: Computation of the difference of topology at infinity for Yamabe-type problems on annuli-domains. I, II
cites work: Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
cites work: Q3709496
cites work: Q3709497
cites work: On a variational problem with lack of compactness: The topological effect of the critical points at infinity
cites work: A Morse lemma at infinity for Yamabe type problems on domains.
cites work: Convergence of solutions of H-systems or how to blow bubbles
cites work: Q5186326
cites work: A multiplicity result for a variational problem with lack of compactness
cites work: The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
cites work: Bifurcation from infinity in a nonlinear elliptic equation involving the limiting Sobolev exponent
cites work: The topological impact of critical points at infinity in a variational problem with lack of compactness: The dimension 3
cites work: A global compactness result for elliptic boundary value problems involving limiting nonlinearities
cites work: Q3275400
DOI: 10.1006/JFAN.1998.3340
description: scientific article; zbMATH DE number 1278793