Positive solutions of some nonlocal boundary value problems
type: Item
instance of: scholarly article
title: Positive solutions of some nonlocal boundary value problems
zbMATH Open document ID: 1072.34014
DOI: 10.1155/S1085337503301034
author: Gennaro Infante
author: J. Webb
published in: Abstract and Applied Analysis
publication date: 2005-04-29T00:00:00Z
full work available at URL: https://eudml.org/doc/51675
review text: For two 4-point BVP \[ u''(t)+g(t)f(u(t))=0\quad \text{a.e. on }[0,1], \] \[ u'(0)=0,\quad u(1)=\alpha_1u(\eta_1)+\alpha_2u(\eta_2), \] or \[ u(0)=0,\quad u(1)=\alpha_1u(\eta_1)+\alpha_2u(\eta_2), \] the authors determine a region in the \((\alpha_1,\,\alpha_2)\)-plane which ensures the existence of positive solutions. Further, they conclude that one can obtain the existence of positive solutions for an \(m\)-point boundary value problem under the weaker assumption that all parameters occurring in the boundary conditions are not required to be positive. Hence, their results allow more general behavior on \(f\) than being either sub- or superlinear.
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 2163631
zbMATH Keywords: m-point boundary value problem
zbMATH Keywords: positive solutions
zbMATH Keywords: existence
reviewed by: Ruyun Ma
MaRDI profile type: Publication
OpenAlex ID: W2023908509
description: scientific article; zbMATH DE number 2163631