Multiplicity of critical points in presence of a linking: application to a superlinear boundary value problem
type: Item
instance of: scholarly article
title: Multiplicity of critical points in presence of a linking: application to a superlinear boundary value problem
zbMATH Open document ID: 1102.35040
author: Dimitri Mugnai
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2004-11-05T00:00:00Z
review text: The author considers the following problem \[ -\Delta u-\lambda u=g(x,u),\text{ in }\Omega\quad u=0,\text{ on }\Omega,\tag{1} \] where \(\Omega\) is a smooth bounded domain of \(\mathbb R^N\), \(N\geq 3\), \(\lambda\in\mathbb R\) and \(g: \Omega\times \mathbb R\to\mathbb R\). The author is interested in a superlinear and subcritical cases. The author shows that for some values of \(\lambda\), problem (1) has at least three nontrivial solutions. To this end the author uses critical point theory.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B38
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 2113836
zbMATH Keywords: multiplicity of solutions
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s00030-004-2016-2
OpenAlex ID: W1970534033
DOI: 10.1007/S00030-004-2016-2
Recommended article: Q592123
Recommended article: A critical points approach to multiplicity results for multi-point boundary value problems
Recommended article: Multiplicity of solutions for critical quasilinear Schrödinger equations using a linking structure
Recommended article: Critical points of solutions to a kind of linear elliptic equations in multiply connected domains
Recommended article: Linking-type results in nonsmooth critical point theory and applications
Recommended article: Q3759165
Recommended article: Multiplicity of solutions for a Dirichlet problem with a singular and a supercritical nonlinearities.
Recommended article: A multiple critical points theorem and applications to quasilinear boundary value problems in \(\mathbf R^N_+\)
Recommended article: Multiplicity results for a superlinear Dirichlet problem
Recommended article: Multiplicity results for a class of superlinear elliptic problems
description: scientific article; zbMATH DE number 2113836