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

Alberto Bressan

doi:10.1016/j.jde.2013.06.019

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

Alberto Bressan

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let F be a continuous multifunction on Rⁿ with compact convex values. For any vector w, let F^w(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)∈F^w(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 language	English (US)
Pages (from-to)	2392-2399
Number of pages	8
Journal	Journal of Differential Equations
Volume	255
Issue number	8
DOIs	https://doi.org/10.1016/j.jde.2013.06.019
State	Published - Oct 15 2013

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jde.2013.06.019

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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",

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doi = "10.1016/j.jde.2013.06.019",

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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).

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

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DO - 10.1016/j.jde.2013.06.019

M3 - Article

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SN - 0022-0396

VL - 255

SP - 2392

EP - 2399

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 8

ER -

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

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