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Baire category and the weak bang-bang property for continuous differential inclusions


Authors: F. S. De Blasi and G. Pianigiani
Journal: Proc. Amer. Math. Soc. 138 (2010), 2413-2423
MSC (2010): Primary 34AXX
Published electronically: March 15, 2010
MathSciNet review: 2607871
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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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Additional Information

F. S. De Blasi
Affiliation: Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy
Email: deblasi@mat.uniroma2.it

G. Pianigiani
Affiliation: Dipartimento di Matematica per le Decisioni, Università di Firenze, Via Lombroso 6/17, 50134 Firenze, Italy
Email: giulio.pianigiani@unifi.it

DOI: https://doi.org/10.1090/S0002-9939-10-10290-1
Received by editor(s): September 8, 2009
Published electronically: March 15, 2010
Communicated by: Yingfei Yi
Article copyright: © Copyright 2010 American Mathematical Society