Global bifurcation and multiple results for Sturm-Liouville problems
type: Item
instance of: scholarly article
title: Global bifurcation and multiple results for Sturm-Liouville problems
zbMATH Open document ID: 1223.34030
author: Yujun Cui
author: Jingxian Sun
author: Yumei Zou
published in: Journal of Computational and Applied Mathematics
publication date: 2011-03-09T00:00:00Z
review text: The following nonlinear Sturm-Liouville boundary value problem \[ \begin{cases} -(p(t)u'(t))' + q(t)u(t) = \lambda a(t)f(u(t)), \quad 0<t<1, \\ \alpha_1 u(0) + \beta_1 u'(0) = 0, \quad \alpha_2 u(1) + \beta_2 u'(1) = 0\end{cases} \] is considered, where \(f\): \({\mathbb R} \to {\mathbb R}\) is a continuous function and there exists \(f_0\), \(f_\infty \in (0,\infty)\) such that \[ f_0 = \lim_{|x|\to0}\, \frac{f(x)}{x}, \quad f_\infty = \lim_{|x|\to\infty} \frac{f(x)}{x}. \] A global bifurcation result is obtained, and then the existence of solutions having exactly \(k-1\) zeros in \((0,1)\) is derived, where \(k \in {\mathbb N}\).
reviewed by: Satoshi Tanaka
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 5863125
zbMATH Keywords: global bifurcation
zbMATH Keywords: Sturm-Liouville problems
MaRDI profile type: Publication
full work available at URL: j.cam.2010.10.014
OpenAlex ID: W2049841435
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DOI: 10.1016/J.CAM.2010.10.014
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description: scientific article; zbMATH DE number 5863125