For continuous differential inclusions the classical bang-bang property is known to fail, yet a weak form of it is established here, in the case where the right hand side is a multifunction whose values are closed convex and bounded sets with nonempty interior contained in a reflexive and separable Banach space. Our approach is based on the Baire category method.
BAIRE CATEGORY AND THE WEAK BANG-BANG PROPERTY FOR CONTINUOUS DIFFERENTIAL INCLUSIONS / F.S. De Blasi; G.Pianigiani. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 138:(2010), pp. 2413-2423.
BAIRE CATEGORY AND THE WEAK BANG-BANG PROPERTY FOR CONTINUOUS DIFFERENTIAL INCLUSIONS
DE BLASI, FRANCESCO SAVERIO;PIANIGIANI, GIULIO
2010
Abstract
For continuous differential inclusions the classical bang-bang property is known to fail, yet a weak form of it is established here, in the case where the right hand side is a multifunction whose values are closed convex and bounded sets with nonempty interior contained in a reflexive and separable Banach space. Our approach is based on the Baire category method.
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