Positive solutions of nonlinear second-order \(m\)-point boundary value problem
type: Item
instance of: scholarly article
title: Positive solutions of nonlinear second-order \(m\)-point boundary value problem
zbMATH Open document ID: 1081.34024
author: Yongping Sun
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-06-01T00:00:00Z
review text: The author presents, under suitable conditions, results concerning the existence of single and multiple positive solutions to the nonlinear second-order \(m\)-point boundary value problem \[ u''(t)+\lambda a(t)f(u(t))=0,\;0<t<1,\quad u(0)=0,\;u(1)=\sum_{i=1}^{m-2}a_iu(\xi_i), \tag{*} \] where \(\lambda>0\) is a parameter, \(a_i \geq 0\) for \(1\leq i \leq m-3\) and \(a_{m-2}>0,\) \(\xi_i\) satisfy \(0<\xi_1<\dots<\xi_{m-2}<1\) and \(\sum_{i=1}^{m-2}a_i\xi_i<1\). An explicit interval is determined such that the existence of at least one positive solution to the boundary value problem (\(*\)) is guaranteed in that interval. The existence of at least two positive solutions of problem (\(*\)) is discussed for an appropriate interval of \(\lambda\). Krasnoselskii's fixed-point theorem of cone expansion-compression type is used to obtain these results.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 2173631
zbMATH Keywords: \(m\)-point boundary value problem
zbMATH Keywords: positive solution
zbMATH Keywords: second-order differential equation
zbMATH Keywords: Krasnoselskii's fixed-point theorem
MaRDI profile type: Publication
full work available at URL: j.na.2005.01.105
OpenAlex ID: W2048281857
cites work: On an M-point boundary value problem
cites work: Solvability of \(m\)-point boundary value problems with nonlinear growth
cites work: Q3994493
cites work: Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation
cites work: Solvability of an \(m\)-point boundary value problem for second order ordinary differential equations
cites work: A sharper condition for the solvability of a three-point second order boundary value problem
cites work: On an m-point boundary-value problem for second-order ordinary differential equations
cites work: Q3820939
cites work: Q3820938
cites work: Q5732050
cites work: Existence theorems for a second order \(m\)-point boundary value problem
cites work: Q4264050
cites work: Positive solutions of a nonlinear \(m\)-point boundary value problem
DOI: 10.1016/J.NA.2005.01.105
description: scientific article; zbMATH DE number 2173631