The critical Neumann problem for semilinear elliptic equations with concave perturbations
type: Item
instance of: scholarly article
title: The critical Neumann problem for semilinear elliptic equations with concave perturbations
zbMATH Open document ID: 1139.35315
published in: Ricerche di Matematica
publication date: 2008-06-24T00:00:00Z
review text: This paper deals with the qualitative analysis of a Neumann semilinear elliptic problem on a bounded domain with smooth boundary. The main feature of this work consists in the presence of a critical nonlinearity (in the Sobolev sense) combined with an indefinite weight function and a concave perturbation. A first result establishes the existence of a solution which is obtained through a local minimization. Next, by means of the concentration-compactness principle and a careful analysis of energy levels of the associated energy functional, the author establishes the existence of a second distinct solution. An interesting relationship between the shape of the variable potential and the mean curvature of the boundary is also established in the present paper.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 35B33
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 5292357
zbMATH Keywords: Neumann problem
zbMATH Keywords: Critical Sobolev exponent
zbMATH Keywords: Concave perturbations
zbMATH Keywords: Multiple solutions
author: Jan Chabrowski
MaRDI profile type: Publication
full work available at URL: s11587-007-0018-1
OpenAlex ID: W2062839923
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DOI: 10.1007/S11587-007-0018-1
description: scientific article; zbMATH DE number 5292357