An exact multiplicity result for a class of symmetric problems
type: Item
instance of: scholarly article
title: An exact multiplicity result for a class of symmetric problems
zbMATH Open document ID: 1362.34041
DOI: 10.4171/PM/1810
author: Philip Korman
published in: Portugaliae Mathematica. Nova Série
publication date: 2008-07-02T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: Summary: We consider positive solutions of a class of semilinear problems \[ u'' + \lambda a(x)f(u) = 0, \quad - 1 < x < 1, \quad u(-1) = u(1) = 0, \] with even and positive \(a(x)\), depending on a positive parameter \(\lambda \). In case \(f(u)\) is convex, an exact multiplicity result was given in our paper with \textit{Y. Li} and \textit{T. Ouyang} [Proc. R. Soc. Edinb., Sect. A, Math. 126, No. 3, 599--616 (1996; Zbl 0855.34022)]. It was observed in our paper with \textit{J. Shi} [Electron. J. Differ. Equ. 2000, 311--322 (2000; Zbl 0970.34015)] that convexity requirement can be relaxed for large \(u\). We show that convexity requirement can also be relaxed for small \(u\).
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B09
zbMATH DE Number: 5296710
zbMATH Keywords: exact multiplicity of solutions
MaRDI profile type: Publication
cites work: Q4816709
OpenAlex ID: W2043619337
description: scientific article; zbMATH DE number 5296710