A three critical points theorem and its applications to the ordinary Dirichlet problem
type: Item
instance of: scholarly article
title: A three critical points theorem and its applications to the ordinary Dirichlet problem
zbMATH Open document ID: 1048.58005
DOI: 10.12775/TMNA.2003.029
author: Diego Averna
author: Gabriele Bonanno
published in: Topological Methods in Nonlinear Analysis
publication date: 2004-09-06T00:00:00Z
review text: In the first part of the present paper the authors establish an abstract result related to the existence of at least three critical points for energy functionals depending on a real parameter \(\lambda\in\Lambda\). They also prove an estimate on the location of the set \(\Lambda\). The main result of this paper generalizes in a nontrivial way the well-known Ricceri's critical point theorem established in [\textit{B. Ricceri}, Arch. Math. 75, No. 3, 220--226 (2000; Zbl 0979.35040)]. In the second part this abstract result is applied to establish a multiplicity result for a class of nonlinear Sturm-Liouville problems. The proofs are based on specific tools of the variational calculus combined with adequate elliptic estimates. Reviewer's remark: The abstract result established in the paper can be applied in the treatment of wide classes of two-point boundary value problems.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 2096718
zbMATH Keywords: critical points
zbMATH Keywords: boundary value problem
zbMATH Keywords: multiplicity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2096718