On the existence of positive solutions for a fourth-order boundary value problem
type: Item
instance of: scholarly article
title: On the existence of positive solutions for a fourth-order boundary value problem
zbMATH Open document ID: 1377.34031
DOI: 10.1155/2017/4946198
author: Yumei Zou
published in: Journal of Function Spaces
publication date: 2017-11-01T00:00:00Z
review text: From the text and introduction: In this paper, we consider the following fourth-order ordinary differential equation boundary value problem: \[ \begin{gathered} u^{(4)}(t)= f(t,u(t), u'(t), u''(t), u'''(t)),\;t\in [0,1],\\ u(0)= u'(0)= u''(1)= u'''(1)= 0,\end{gathered} \] where \(f:[0,1]\times \mathbb{R}^3_+\times \mathbb{R}_-\to \mathbb{R}\), is continuous. By using the method of order reduction and the fixed point index, the existence of positive solutions is studied. We provide conditions under which the existence results hold. Such conditions are related to the frst eigenvalue corresponding to the relevant linear differential equation with dependence on the derivatives of the unknown function.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 6802004
zbMATH Keywords: fixed point index
zbMATH Keywords: first eigenvalue
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/4946198
OpenAlex ID: W2748140393
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description: scientific article; zbMATH DE number 6802004