Positive solutions of three-point boundary value problems for higher-order \(p\)-Laplacian with infinitely many singularities
type: Item
instance of: scholarly article
title: Positive solutions of three-point boundary value problems for higher-order \(p\)-Laplacian with infinitely many singularities
zbMATH Open document ID: 1148.34022
DOI: 10.1155/DDNS/2006/69073
author: Yunming Zhou
author: Fuyi Xu
author: Yonghong Wu
author: Lishan Liu
published in: Discrete Dynamics in Nature and Society
publication date: 2008-07-28T00:00:00Z
full work available at URL: https://eudml.org/doc/129318
review text: Summary: We study the higher-order quasilinear equation with \(p\)-Laplacian \[ (\phi_p(u^{(n-1)}))'+g(t)f(t,u,u',\dots,u^{(n-2)})=0,\quad 0<t<1,\;n\geq3, \] subject to the following three-point boundary conditions: \[ \begin{aligned} u^i(0) = 0,\quad & 0\leq i\leq n - 3,\\ \alpha\phi_p(u^{(n-2)}(0))&-\beta\phi_p(u^{(n-1)}(\eta))=0,\\ \gamma\phi_p(u^{(n-2)}(1))&-\delta\phi_p(u^{(n-1)}(1))=0,\end{aligned} \] where \(\phi_p(s)\) is a \(p\)-Laplacian operator, that is, \(\phi_p(s)= |s|^{p-2}s\), \(p > 1\), \(\eta\in (0,1)\) is a given constant, \(\alpha > 0\), \(\gamma > 0\), \(\beta\geq 0\), \(\delta\geq 0\), \(g : [0,1] \to [0,\infty)\) has countable many singularities on \((0,1/2)\). We show that there exist countable many positive solutions by using the fixed point index theorem for operators in a cone.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5304374
MaRDI profile type: Publication
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OpenAlex ID: W2085077829
description: scientific article; zbMATH DE number 5304374