Publication Cover
Applicable Analysis
An International Journal
Volume 5, 1975 - Issue 2
62
Views
36
CrossRef citations to date
0
Altmetric
Original Articles

Flow-invariant sets and differential inequalities in normed spacesFootnote

&
Pages 149-161 | Published online: 02 May 2007
 

Abstract

A set M in a Banach space B is said to be flow-invariant with respect to the ordinary differential equation x(t)=f(t,x) (t real, xεB,f(t,x)εB), if for each solution x(i) of this equation x(0) ε M implies x(t) ε M for t >0. In this paper, several theorems on flow-invariance are given. These theorems on differential inequalities in ordered Banach spaces. In particular, they apply to the important case when the interior of the positive cone of the Banach space is empty. Finally it is shown that the basic assumption for the validity of a theorem on differential inequalities, namely the quasimonotonicity property as given by Volkmann [11], is equivalent to the tangent condition of Brezis [3]with respect to the positive cone.

Dedicated to Professor Johannes Weissinger on the occasion of his sixtieth birthday

Dedicated to Professor Johannes Weissinger on the occasion of his sixtieth birthday

Notes

Dedicated to Professor Johannes Weissinger on the occasion of his sixtieth birthday

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.