Concentration of solutions for the scalar curvature equation on \(\mathbb{R}^n\)
type: Item
instance of: scholarly article
title: Concentration of solutions for the scalar curvature equation on \(\mathbb{R}^n\)
zbMATH Open document ID: 0954.35058
author: Shusen Yan
published in: Journal of Differential Equations
publication date: 2001-02-01T00:00:00Z
review text: The paper deals with the scalar curvature equation \[ \begin{cases}-\Delta u=K(y)u^{2^\star-1-j},\qquad & y\in{\mathbb{R}}^N, \\ u>0, & y\in{\mathbb{R}}^N, \\ u\to 0, & \text{as\;}\left|y\right|\to 0,\end{cases} \] with \(2^\star={{2N}\over{N-2}}\) and \(N\geq 3\). The author establishes the existence of infinitely many solutions if there is a sequence \((z_j)\in({\mathbb{R}}^{N})^{\mathbb{N}}\) with \(\left|z_j\right|\to\infty\) such that \(K\) has strict local maxima at those \(z_j\). A perturbation result is also derived, and it is observed that the case \(N=3\) allows slightly sharper versions of the results.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B20
zbMATH DE Number: 1474622
zbMATH Keywords: infinitely many solutions
zbMATH Keywords: perturbation
reviewed by: Georg Hetzer
MaRDI profile type: Publication
full work available at URL: jdeq.1999.3718
OpenAlex ID: W2080229835
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DOI: 10.1006/JDEQ.1999.3718
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description: scientific article; zbMATH DE number 1474622