Symmetric and nonsymmetric solutions for an elliptic equation on \(\mathbb R^N\)
type: Item
instance of: scholarly article
title: Symmetric and nonsymmetric solutions for an elliptic equation on \(\mathbb R^N\)
zbMATH Open document ID: 1127.35015
author: Sebastián Lorca
author: Pedro Ubilla
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-10-01T00:00:00Z
review text: The authors establish the existence of a positive solution, as well as that of nonradial solutions, which changes sign, for nonlinear elliptic problem \[ -\Delta u+V(z)u=f(z,u)\quad u\in H^1(\mathbb R^N),\tag{1} \] where \(V:\mathbb R^N\to\mathbb R\) is a given non-negative potential and \(f\), \(f:\mathbb R^N\times\mathbb R\to\mathbb R\) is a Hölder continuous function. Under some additional assumptions on \(V\) and \(f\), the authors show that the problem (1) has two nontrivial solutions.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 47J30
zbMATH DE Number: 2105457
zbMATH Keywords: positive solution
zbMATH Keywords: nonradial solutions
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.na.2004.03.034
OpenAlex ID: W2081163974
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DOI: 10.1016/J.NA.2004.03.034
description: scientific article; zbMATH DE number 2105457