Two positive solutions of third-order BVP with integral boundary condition and sign-changing Green's function
type: Item
instance of: scholarly article
title: Two positive solutions of third-order BVP with integral boundary condition and sign-changing Green's function
zbMATH Open document ID: 1321.34040
DOI: 10.1155/2015/491423
author: Bing-Wei Niu
author: Qiu-Yan Ren
author: Jian-Ping Sun
published in: Journal of Function Spaces
publication date: 2015-08-20T00:00:00Z
review text: Summary: We are concerned with the following third-order boundary value problem with integral boundary condition: \[ u'''(t)= f(t,u(t)),\;t\in [0,1], \] \[ u'(0)= u(1)= 0,\;u''(\eta)+ \int^\beta_\alpha u(t)\,dt= 0, \] where \(1/2< \alpha\leq\beta\leq 1\), \(\alpha+\beta\leq 4/3\), and \(\eta\in(1/2, \alpha]\). Although the corresponding Greens 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. An example is also included to illustrate the main results obtained.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B27
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6474217
Wikidata QID: Q59112840
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/491423
OpenAlex ID: W1498660237
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description: scientific article; zbMATH DE number 6474217