Morse theory and multiple positive solutions to a Neumann problem
type: Item
instance of: scholarly article
title: Morse theory and multiple positive solutions to a Neumann problem
zbMATH Open document ID: 0849.35034
DOI: 10.1007/BF01759261
author: M. Lazzo
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1996-11-14T00:00:00Z
review text: The author proves multiplicity results for the semilinear elliptic Neumann problem \[ - d \Delta u+ u= u^{p- 1},\quad u> 0\quad \text{in } \Omega,\;\partial u/\partial\nu= 0\text{ on } \partial\Omega,\tag{1} \] where \(\Omega\) is a bounded domain and \(p> 2\) is subcritical. By relating the Poincaré polynomial of the boundary of \(\Omega\), \(P_t(\partial\Omega)\), to that of certain energy levels of the associated functional of (1), she proves that (1) has at least \(2P_1(\partial\Omega)\) nonconstant solutions (counted with multiplicity).
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 878449
zbMATH Keywords: homology of the boundary
zbMATH Keywords: semilinear elliptic equation
zbMATH Keywords: multiplicity
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01759261
OpenAlex ID: W2021188494
description: scientific article; zbMATH DE number 878449