Nonlinear bang-bang principle in \({\mathbb{R}}^ n\)
type: Item
instance of: scholarly article
title: Nonlinear bang-bang principle in \({\mathbb{R}}^ n\)
zbMATH Open document ID: 0733.34026
DOI: 10.1007/BF01142650
author: S. I. Suslov
published in: Mathematical Notes
publication date: 1991-01-01T00:00:00Z
review text: In the paper some interrelations between the sets A and B of all solutions of the Cauchy problems (1) \(\dot x\in F(t,x)\), \(x(0)=0\), \(t\in T\subset [0,1]\), \(x\in {\mathbb{R}}^ n\), (2) \(\dot x\in extr.F(t,x)\), \(x(0)=0\) are studied. It is assumed that F(\(\cdot,\cdot)\) is measurable in t, lipschitzian in x, has compact and convex values and that the function \(t\to \sup \{\| x\|:\) \(x\in F(t,0)\}\) is measurable and bounded. It is proved that the set B is dense in the set A. In the proof the Baire category theorem is used.
reviewed by: Z.Wyderka
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 4212492
zbMATH Keywords: differential inclusions
zbMATH Keywords: bang-bang principle
zbMATH Keywords: Cauchy problems
zbMATH Keywords: Baire category theorem
MaRDI profile type: Publication
cites work: Q3324260
cites work: Q4692346
cites work: Q3889652
cites work: Q4256552
cites work: Q3319056
cites work: Measurable relations
cites work: Convex analysis and measurable multifunctions
cites work: Integrals of set-valued functions
description: scientific article; zbMATH DE number 4212492