Positive solutions of higher-order four-point boundary value problem with \(p\)-Laplacian operator
type: Item
instance of: scholarly article
title: Positive solutions of higher-order four-point boundary value problem with \(p\)-Laplacian operator
zbMATH Open document ID: 1194.34035
author: Hongyun Wu
author: Jihui Zhang
published in: Journal of Computational and Applied Mathematics
publication date: 2010-03-04T00:00:00Z
review text: The authors consider the existence of positive solutions for a four-point singular boundary value problem of the form \[ \begin{aligned} &(\phi_p(u^{(n-1)}(t)))'+a(t)f(u(t),u'(t),\dots,u^{(n-1)}(t))=0,\quad t\in(0,1),\\ &u^{(i)}(0)=0,\quad 0\leq i\leq n-3,\\ &\lambda_1\phi_p(u^{(n-2)}(0))-\mu_1\phi_p(u^{(n-1)}(\xi))=0,\\ &\lambda_2\phi_p(u^{(n-2)}(1))+\mu_2\phi_p(u^{(n-1)}(\eta))=0, \end{aligned} \] where \(\phi_p(s)=|s|^{p-2}s,\;p>1\). By means of the fixed point theorem due to Bai and Ge, some sufficient conditions for the existence of positive solutions are presented.
reviewed by: Minghe Pei
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B16
zbMATH DE Number: 5677323
zbMATH Keywords: four-point singular boundary value problem
zbMATH Keywords: \(p\)-Laplacian operator
zbMATH Keywords: positive solutions
zbMATH Keywords: fixed point theorem
MaRDI profile type: Publication
full work available at URL: j.cam.2009.06.040
OpenAlex ID: W2074401034
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DOI: 10.1016/J.CAM.2009.06.040
description: scientific article; zbMATH DE number 5677323