Infinitely many radial solutions of a semilinear elliptic problem on \(\mathbb{R}^ N\)
type: Item
instance of: scholarly article
title: Infinitely many radial solutions of a semilinear elliptic problem on \(\mathbb{R}^ N\)
zbMATH Open document ID: 0790.35020
DOI: 10.1007/BF00953069
published in: Archive for Rational Mechanics and Analysis
publication date: 1994-01-23T00:00:00Z
review text: The authors construct infinitely many radial solutions of the problem \(- \Delta u+ b(| x|)u= f(| x|,u)\) on \(\mathbb{R}^ N\) for suitable \(b\) and \(f\). They in fact prove that there is a solution with \(k\) zeros for any positive integer \(k\). They first construct positive and negative solutions and then construct the other solutions by a method of Nehari type [cf. \textit{Z. Nehari}, Acta Math. 105, 141-175 (1961; Zbl 0099.291)].
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 484800
zbMATH Keywords: variational methods
zbMATH Keywords: infinitely many radial solutions
author: Thomas J. Bartsch
author: Michel Willem
reviewed by: E. N. Dancer
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00953069
OpenAlex ID: W2062270670
description: scientific article; zbMATH DE number 484800