Fixed points of increasing operators in ordered space with applications.
type: Item
instance of: scholarly article
title: Fixed points of increasing operators in ordered space with applications.
zbMATH Open document ID: 1035.47028
DOI: 10.1007/BF02438341
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2002-01-01T00:00:00Z
review text: This article deals with some modifications of well-known results about minimal-maximal fixed points of increasing operators in ordered spaces. As applications, the following boundary value problem: \[ \ddot x+f(t,x)=0,\quad a<t<b, \] \[ ax(a)-\beta\dot x(a) =0,\;\gamma x(b)+\delta\dot x(b)=0,\;(\alpha,\beta,\gamma, \delta\geq 0, (b-a)\alpha\gamma+ \alpha\delta+ \beta\gamma>0) \] is considered. The author formulates some natural conditions for the existence of minimal-maximal solutions to this problem, assuming that the function \(f(t,\cdot)\) is increasing without any assumptions on continuity, compactness, convexity or concavity.
Mathematics Subject Classification ID: 47H07
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B16
zbMATH DE Number: 1810313
zbMATH Keywords: existence of solutions
zbMATH Keywords: minimal-maximal fixed points
zbMATH Keywords: increasing operators
zbMATH Keywords: ordered spaces
zbMATH Keywords: boundary value problem
author: Guang Chong Yang
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
cites work: Q4501374
cites work: Uniqueness of positive solutions for singular nonlinear second-order boundary-value problems
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cites work: Quasi-weak convergence with applications in ordered Banach space
full work available at URL: https://doi.org/10.1007/bf02438341
OpenAlex ID: W2120466299
description: scientific article; zbMATH DE number 1810313