Multiple positive solutions for an \(n\)-point nonhomogeneous boundary value problems in Banach spaces
type: Item
instance of: scholarly article
title: Multiple positive solutions for an \(n\)-point nonhomogeneous boundary value problems in Banach spaces
zbMATH Open document ID: 1242.34111
author: Haibo Chen
author: Yusen Wu
author: Peiluan Li
published in: Results in Mathematics
publication date: 2010-11-17T00:00:00Z
review text: The authors investigate the following \(n\)-point nonhomogeneous BVP \[ \begin{aligned} &u''(t)+a(t)f(t,u(t))=\theta, \;\;t\in (0,1), \\ &u(0)=\theta, \;\;u(1)-\sum_{i=1}^{n-2}k_iu(\xi_i)=b \end{aligned} \] in a Banach space \(E\), where \(\theta\) is the zero element of \(E\), \(b\in E\), \(f\in C[I\times E,\,E]\), \(I=[0,1]\) and \(0<\xi_1<\xi_2<\cdots<\xi_{n-2}<1,\;k_i>0\) \((i=1,2,\dots,m-2)\). By using the fixed point theorem of strict-set-contractions, they derive some sufficient conditions for the existence of at least one or two positive solutions for the problem.
reviewed by: Yulian An
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5816638
zbMATH Keywords: boundary value problem
zbMATH Keywords: Banach space
zbMATH Keywords: positive solution
zbMATH Keywords: fixed point theorem
MaRDI profile type: Publication
full work available at URL: s00025-010-0037-1
OpenAlex ID: W2084145879
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DOI: 10.1007/S00025-010-0037-1
description: scientific article; zbMATH DE number 5816638