Symmetric positive solutions for nonlinear singular fourth-order eigenvalue problems with nonlocal boundary condition
type: Item
instance of: scholarly article
title: Symmetric positive solutions for nonlinear singular fourth-order eigenvalue problems with nonlocal boundary condition
zbMATH Open document ID: 1196.34028
DOI: 10.1155/2010/187827
author: Jian Liu
author: Fuyi Xu
published in: Discrete Dynamics in Nature and Society
publication date: 2010-04-26T00:00:00Z
full work available at URL: https://eudml.org/doc/230306
review text: By using a fixed point theorem in cones, the authors prove the existence of symmetric positive solutions of the fourth-order nonlocal boundary value problem \[ \begin{cases} u^{(4)}(t)-\lambda h(t)f(t,u,u'')=0,\,\,\,0<t<1,\\ u(0)=u(1)=\displaystyle\int_0^1a(s)u(s)\,ds,\\ u''(0)=u''(1)=\displaystyle\int_0^1b(s)u''(s)\,ds,\end{cases} \] where \(a,\,b\in L^1[0,1]\), \(\lambda>0\), \(h\) may be singular at \(t=0\) and/or \(t=1\) and \(f(t,x,y)\) may also have singularities at \(x=0\) and/or \(y=0\).
reviewed by: Rodica Luca
Mathematics Subject Classification ID: 34B09
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 5701479
zbMATH Keywords: fourth-order eigenvalue equation
zbMATH Keywords: nonlocal boundary conditions
zbMATH Keywords: existence of solutions
zbMATH Keywords: symmetric solutions
zbMATH Keywords: positive solutions
zbMATH Keywords: fixed point theorem
Wikidata QID: Q58650749
MaRDI profile type: Publication
OpenAlex ID: W2065089810
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description: scientific article; zbMATH DE number 5701479