Exact multiplicity of boundary blow-up solutions for a bistable problem
type: Item
instance of: scholarly article
title: Exact multiplicity of boundary blow-up solutions for a bistable problem
zbMATH Open document ID: 1152.34017
author: Junping Shi
author: Shin-Hwa Wang
publication date: 2008-06-12T00:00:00Z
review text: The paper concerns the exact multiplicity of positive solutions \(u\leq 1/n\) of the problem \[ u''(x)+\lambda f(u(x))=0 \quad (-1<x<1), \qquad u(-1)=u(1)=1/n\in (1,\infty], \] where \(\lambda>0\), \(0\leq n<1\), and \(f(u)=u(u-\sigma)(1-u)\) \((\sigma\in (1/2,1))\). By using the time-mapping method (quadrature method), the authors prove that there exists \(\lambda^\ast>0\) such that the problem has exactly three solutions for \(\lambda>\lambda^\ast\), exactly two solutions for \(\lambda=\lambda^\ast\), and exactly one solution for \(\lambda<\lambda^\ast\).
reviewed by: Jin Liang
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 5288028
zbMATH Keywords: boundary blow-up solution
zbMATH Keywords: exact multiplicity
zbMATH Keywords: time-mapping
zbMATH Keywords: bistable
MaRDI profile type: Publication
full work available at URL: j.camwa.2007.04.017
OpenAlex ID: W2114648064
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DOI: 10.1016/J.CAMWA.2007.04.017
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 5288028