The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds
type: Item
instance of: scholarly article
title: The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds
zbMATH Open document ID: 1161.58310
author: Angela Pistoia
author: Anna Maria Micheletti
published in: Calculus of Variations and Partial Differential Equations
publication date: 2009-03-24T00:00:00Z
review text: Let \((M, g)\) be a smooth compact Riemannian \(N\)-manifold, \(N \geq 2,\) and \(p > 2\) if \(N = 2\) and \({2 < p < 2^{*} = {2N \over N-2}}\) if \(N \geq 3.\) The authors show that the positive solutions of the problem \[ -\varepsilon^2\Delta_g u + u = u^{p-1}\quad \text{in}\;M \] are generated by stable critical points of the scalar curvature of \(g,\) if \(\varepsilon\) is small enough.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 58E30
zbMATH DE Number: 5532488
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: scalar curvature
zbMATH Keywords: nonlinear elliptic equation
Wikidata QID: Q115387626
MaRDI profile type: Publication
full work available at URL: s00526-008-0183-4
OpenAlex ID: W2006934881
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DOI: 10.1007/S00526-008-0183-4
description: scientific article; zbMATH DE number 5532488