Maximum principles for ordinary differential inequalities of fourth and sixth order
type: Item
instance of: scholarly article
title: Maximum principles for ordinary differential inequalities of fourth and sixth order
zbMATH Open document ID: 0699.34015
DOI: 10.1016/0022-247X(90)90312-4
author: Ahmed Mohammed
author: Giovanni Porru
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: The authors extend the maximum principle for second order differential inequalities to certain classes of differential inequalities of fourth and sixth order. For example, let \(L_ iu=u''+f_ i(x)u'+h_ i(x)u,\) \(i=1,2\), where \(f_ 1\), \(h_ 1\) are continuous on (a,b) and \(f_ 2,h_ 2\) are of class \(C^ 2(a,b)\). Let \(h_ i(x)\leq 0\), \(i=1,2\). If \(u\in C^ 4(a,b)\cap C^ 1[a,b]\) satisfies the differential inequalities \(L_ 1L_ 2u\geq 0\), \(u'(a)\geq 0\), \(u'(b)\leq 0\) and if u assumes zero as a minimum at a point in (a,b), then \(u(x)=0\) on [a,b].
Mathematics Subject Classification ID: 34A40
zbMATH DE Number: 4146427
zbMATH Keywords: maximum principle
zbMATH Keywords: second order differential inequalities
reviewed by: Kenneth S. Miller
MaRDI profile type: Publication
cites work: A maximum principle for fourth order ordinary differential equations
cites work: Maximum principles for fourth order ordinary differential inequalities
cites work: Q5533735
full work available at URL: 0022-247x(90)90312-4
OpenAlex ID: W1986626761
description: scientific article; zbMATH DE number 4146427