Baire category and the weak bang-bang property for continuous differential inclusions
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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.References
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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
- Received by editor(s): September 8, 2009
- Published electronically: March 15, 2010
- Communicated by: Yingfei Yi
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 2413-2423
- MSC (2010): Primary 34AXX
- DOI: https://doi.org/10.1090/S0002-9939-10-10290-1
- MathSciNet review: 2607871