The Dirichlet problem for quasimonotone systems of second order equations
type: Item
instance of: scholarly article
title: The Dirichlet problem for quasimonotone systems of second order equations
zbMATH Open document ID: 1089.34018
author: Gerd Herzog
published in: Rocky Mountain Journal of Mathematics
publication date: 2004-09-27T00:00:00Z
review text: Let \(E\) be a finite-dimensional real vector space ordered by a solid cone. Consider the Dirichlet boundary value problem \[ u''(t)=f\bigl(t,u(t) \bigr),\;t\in[0,1],\;u(0)=u(1)=0,\tag{D} \] where \(f:[0,1]\times E\to E\) is continuous and quasimonotone in \(u\) for \(t\in[0,1]\). Using the method of lower and upper solutions, the author proves the existence of a solution \(u\in C^2([0,1],E)\) of (D).
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 2103623
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069899
OpenAlex ID: W2021285443
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DOI: 10.1216/RMJM/1181069899
description: scientific article; zbMATH DE number 2103623