Existence theorems for a second order nonlinear differential equation with nonlocal boundary conditions and their applications
type: Item
instance of: scholarly article
title: Existence theorems for a second order nonlinear differential equation with nonlocal boundary conditions and their applications
zbMATH Open document ID: 1205.34019
author: Xuemei Zhang
author: Weigao Ge
author: Meiqiang Feng
published in: Journal of Applied Mathematics and Computing
publication date: 2010-06-29T00:00:00Z
review text: Let \(w\in L^p(0,1)\) and \(\lambda\) be a parameter. The authors considered the second-order differential equation \[ \lambda u''(t)-w(t) f(t, u(t))=0 \] subject to one of the following sets of conditions: a. \(x(0)=x(1)=\int^1_0 g(t)x(t)\,dt\); b. \(x(0)=\int^1_0 g(t)x(t)\,dt\), \(x(1)=0\); c. \(x(0)=0\), \(x(1)=\int^1_0 g(t)x(t)\,dt\). By applying Hölder's inequality and fixed point theory in cones, they prove the existence and multiplicity of positive solutions of the above problems.
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5728291
zbMATH Keywords: nonlocal boundary value problems
zbMATH Keywords: fixed point index
zbMATH Keywords: integral boundary conditions
zbMATH Keywords: positive solutions
zbMATH Keywords: existence
Wikidata QID: Q115377235
reviewed by: Ruyun Ma
MaRDI profile type: Publication
full work available at URL: s12190-009-0278-x
OpenAlex ID: W2015896303
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DOI: 10.1007/S12190-009-0278-X
description: scientific article; zbMATH DE number 5728291