Positive solutions of a third-order three-point BVP with sign-changing Green's function
type: Item
instance of: scholarly article
title: Positive solutions of a third-order three-point BVP with sign-changing Green's function
zbMATH Open document ID: 1407.34038
DOI: 10.1155/2014/406815
author: Li-Juan Gao
author: Jian-Ping Sun
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: We are concerned with the following third-order three-point boundary value problem: \(u^{\prime \prime \prime} \left(t\right) = f \left(t, u \left(t\right)\right), t \in \left[0, 1\right], u'\left(0\right) = u \left(1\right) = 0\) and \(u^{\prime \prime} \left(\eta\right) - \alpha u'\left(1\right) = 0,\) where \(\alpha \in \left[0, 1\right)\) and \(\eta \in \left[(14 + \alpha) /(24 - 3 \alpha), 1\right)\). Although the corresponding Green's function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions on \(f\) by using the two-fixed-point theorem due to Avery and Henderson.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 7016364
Wikidata QID: Q59066830
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/406815
OpenAlex ID: W1986528922
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description: scientific article; zbMATH DE number 7016364