Extremal solutions of differential inclusions via Baire category: A dual approach

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let F be a continuous multifunction on Rn with compact convex values. For any vector w, let Fw(x)⊆F(x) be the subset of points which maximize the inner product with w. Call W the set of all continuous functions w:[0,T]{mapping}Rn with the following property: all solutions to the Cauchy problem ẋ(t)∈Fw(t)(x(t)), x(0) = 0, are also solutions to ẋ(t)∈extF(x(t)). We prove that W is residual in C([0,T]; Rn).

Original languageEnglish (US)
Pages (from-to)2392-2399
Number of pages8
JournalJournal of Differential Equations
Volume255
Issue number8
DOIs
StatePublished - Oct 15 2013

Fingerprint

Baire Category
Extremal Solutions
Differential Inclusions
Scalar, inner or dot product
Cauchy Problem
Continuous Function
Maximise
Subset

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

@article{1ae1eba0607a45d9a134eba67b5d70e2,
title = "Extremal solutions of differential inclusions via Baire category: A dual approach",
abstract = "Let F be a continuous multifunction on Rn with compact convex values. For any vector w, let Fw(x)⊆F(x) be the subset of points which maximize the inner product with w. Call W the set of all continuous functions w:[0,T]{mapping}Rn with the following property: all solutions to the Cauchy problem ẋ(t)∈Fw(t)(x(t)), x(0) = 0, are also solutions to ẋ(t)∈extF(x(t)). We prove that W is residual in C([0,T]; Rn).",
author = "Alberto Bressan",
year = "2013",
month = "10",
day = "15",
doi = "10.1016/j.jde.2013.06.019",
language = "English (US)",
volume = "255",
pages = "2392--2399",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "8",

}

Extremal solutions of differential inclusions via Baire category : A dual approach. / Bressan, Alberto.

In: Journal of Differential Equations, Vol. 255, No. 8, 15.10.2013, p. 2392-2399.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Extremal solutions of differential inclusions via Baire category

T2 - A dual approach

AU - Bressan, Alberto

PY - 2013/10/15

Y1 - 2013/10/15

N2 - Let F be a continuous multifunction on Rn with compact convex values. For any vector w, let Fw(x)⊆F(x) be the subset of points which maximize the inner product with w. Call W the set of all continuous functions w:[0,T]{mapping}Rn with the following property: all solutions to the Cauchy problem ẋ(t)∈Fw(t)(x(t)), x(0) = 0, are also solutions to ẋ(t)∈extF(x(t)). We prove that W is residual in C([0,T]; Rn).

AB - Let F be a continuous multifunction on Rn with compact convex values. For any vector w, let Fw(x)⊆F(x) be the subset of points which maximize the inner product with w. Call W the set of all continuous functions w:[0,T]{mapping}Rn with the following property: all solutions to the Cauchy problem ẋ(t)∈Fw(t)(x(t)), x(0) = 0, are also solutions to ẋ(t)∈extF(x(t)). We prove that W is residual in C([0,T]; Rn).

UR - http://www.scopus.com/inward/record.url?scp=84881046798&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84881046798&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2013.06.019

DO - 10.1016/j.jde.2013.06.019

M3 - Article

AN - SCOPUS:84881046798

VL - 255

SP - 2392

EP - 2399

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 8

ER -