A multiplicity result of positive solutions for third-order multi-point boundary value problem
type: Item
instance of: scholarly article
zbMATH Open document ID: 1284.34034
author: Qiao Zongmin
author: Liu Yang
publication date: 2013-08-22T00:00:00Z
full work available at URL: http://www.math.ubbcluj.ro/~nodeacj/download.php
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6200646
zbMATH Keywords: multi-point boundary value problem
zbMATH Keywords: positive solution
zbMATH Keywords: cone
zbMATH Keywords: fixed point
MaRDI profile type: Publication
title: A multiplicity result of positive solutions for third-order multi-point boundary value problem
published in: Fixed Point Theory
review text: Consider the boundary value problem NEWLINE\[NEWLINE\begin{gathered} x'''(t)= f(t,x(t), x'(t), x''(t))\quad\text{for }t\in (0,1),\\ x''(1)= 0,\;x'(1)= 0,\;x(0)= \sum^{m-2}_{i=1} \beta_i x(\xi_i),\end{gathered}\tag{\(*\)}NEWLINE\]NEWLINE where \(0<\xi_1<\xi_2<\cdots< \xi_{m-2}< 1\), \(0<\beta_i< 1\) for \(1\leq i\leq m-2\), \(\sum^{m-2}_{i=1} \beta_i< 1\), \(f\in C((0,1)\times \mathbb{R}^3,[0,+ \infty))\).NEWLINENEWLINE The authors use the fixed point theorem due to Avery and Peterson to establish the existence of at least three positive solutions to \((*)\).
reviewed by: Klaus R. Schneider
description: scientific article; zbMATH DE number 6200646