Multiple positive solutions for a three-point boundary value problem
type: Item
instance of: scholarly article
title: Multiple positive solutions for a three-point boundary value problem
zbMATH Open document ID: 0906.34014
DOI: 10.1016/S0895-7177(98)00028-4
published in: Mathematical and Computer Modelling
publication date: 1998-06-11T00:00:00Z
review text: The author deals with the three-point boundary value problem \[ -x'''+ f(x(t))= 0,\quad x(0)= x'(t_2)= x''(1)= 0\tag{1} \] with \(t_2\in\left[{1\over 2},1\right)\), \(f: \mathbb{R}\to \mathbb{R}\) is continuous and nonnegative for \(x\geq 0\). Using properties of the Green function of the corresponding linear problem and a theorem by \textit{R. W. Leggett} and \textit{L. R. Williams} [Indiana Univ. Math. J. 28, 673-688 (1979; Zbl 0421.47033)], the author proves the existence of at least three positive solutions to (1).
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B27
zbMATH DE Number: 1164061
zbMATH Keywords: multipoint BVP
zbMATH Keywords: third-order ODE
zbMATH Keywords: Green function
zbMATH Keywords: fixed point
zbMATH Keywords: cone
author: Douglas R. Anderson
reviewed by: Irena Rachůnková
MaRDI profile type: Publication
cites work: Double positive solutions of \((n,p)\) boundary value problems for higher order difference equations
cites work: Three positive solutions to a discrete focal boundary value problem
cites work: Existence of multiple positive solutions to a conjugate boundary value problem
cites work: Q4526467
cites work: Singular nonlinear boundary value problems for higher order ordinary differential equations
cites work: Multiple positive solutions of some boundary value problems
cites work: On the Existence of Positive Solutions of Ordinary Differential Equations
cites work: Q5330830
cites work: Q3854213
cites work: Q3994493
full work available at URL: s0895-7177(98)00028-4
OpenAlex ID: W2026343039
description: scientific article; zbMATH DE number 1164061