Multiple solutions of impulsive Sturm-Liouville boundary value problem via lower and upper solutions and variational methods
type: Item
instance of: scholarly article
title: Multiple solutions of impulsive Sturm-Liouville boundary value problem via lower and upper solutions and variational methods
zbMATH Open document ID: 1241.34032
author: Yu Tian
author: Weigao Ge
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-01-04T00:00:00Z
review text: The authors consider the impulsive Sturm-Liouville boundary value problem \[ \begin{aligned} &-Lu = f(x,u), \quad x \in [0,1]\setminus\{x_1,\dots,x_\ell\},\\ &-\Delta(p(x_i)u'(x_i)) = I_i(u(x_i)), \quad i = 1,\dots,\ell,\\ &R_1(u) = 0, \quad R_2(u) = 0, \end{aligned} \] where \(Lu = (p(x)u')' - q(x)u\) is a Sturm-Liouville operator, \(R_1(u) = \alpha u'(0) - \beta u(0)\), \(R_2(u) = \gamma u'(1) + \sigma u(1)\), \(0 < x_1 < \dots < x_\ell < 1\). Using lower and upper solutions method and variational methods, there is obtained an existence result for at least four solutions of the BVP.
reviewed by: Jan Tomeček
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 58E50
zbMATH DE Number: 5994315
zbMATH Keywords: multiple solutions
zbMATH Keywords: impulsive Sturm-Liouville boundary value problem
zbMATH Keywords: critical point
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: variational methods
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.08.042
OpenAlex ID: W2091837355
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DOI: 10.1016/J.JMAA.2011.08.042
description: scientific article; zbMATH DE number 5994315