Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow
type: Item
instance of: scholarly article
title: Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow
zbMATH Open document ID: 1100.35008
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-04-06T00:00:00Z
review text: In the present study the authors obtain sing-changing solutions of the problem: \[ -\left(a+b\int_\Omega|\nabla u|^2\,dx\right)\Delta u=f (x,u),\quad \text{in }\Omega, \qquad u=0,\quad\text{on }\partial\Omega,\tag{1} \] where \(\Omega\) is a smooth bounded domain in \(\mathbb{R}^N\), \(a,b>0\) and \(f\) is a given function. Under suitable assumptions on the data, the authors obtain sign-changing solutions for (1). To this end, they use variational methods and invariant sets of descent flow.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 5017393
zbMATH Keywords: nonlocal problems
zbMATH Keywords: variational methods
author: Zhitao Zhang
author: Kanishka Perera
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.06.102
OpenAlex ID: W2116032482
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DOI: 10.1016/J.JMAA.2005.06.102
description: scientific article; zbMATH DE number 5017393