Existence of solutions for fourth order differential equation with four-point boundary conditions
type: Item
instance of: scholarly article
title: Existence of solutions for fourth order differential equation with four-point boundary conditions
zbMATH Open document ID: 1140.34308
author: Chuanzhi Bai
author: Dandan Yang
author: Hongbo Zhu
published in: Applied Mathematics Letters
publication date: 2008-02-14T00:00:00Z
review text: The authors study the fourth order differential equation \[ u^{(4)}(t)=f(t,u(t)), \; t \in (0,1), \] subject to the boundary conditions \[ \begin{gathered} u(0)=0,\quad au''(\xi_1)-bu'''(\xi_1)=0,\\ u(1)=0,\quad cu''(\xi_2)-du'''(\xi_2)=0, \end{gathered} \] where \(0\leq \xi_1 \leq \xi_2\leq 1\). They prove that this boundary value problem (BVP) has a solution. The main ingredient of the proof is a nonlinear alternative theorem of Leray-Schauder-type. The authors also give some remarks on a paper by \textit{S. Chen}, \textit{W. Ni} and \textit{C. Wang} [ Appl. Math. Lett. 19, 161-168 (2006; Zbl 1096.34009)], where this particular BVP has been studied previously.
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5235070
zbMATH Keywords: Boundary value problem
zbMATH Keywords: fixed point
zbMATH Keywords: nonlinear alternative
reviewed by: Gennaro Infante
MaRDI profile type: Publication
full work available at URL: j.aml.2006.11.013
OpenAlex ID: W2072481813
Wikidata QID: Q115360957
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DOI: 10.1016/J.AML.2006.11.013
description: scientific article