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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Upper semicontinuous differential inclusions without convexity


Authors: A. Bressan, A. Cellina and G. Colombo
Journal: Proc. Amer. Math. Soc. 106 (1989), 771-775
MSC: Primary 34A60; Secondary 49E10
MathSciNet review: 969314
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove existence of solutions to the Cauchy problem for the differential inclusion $ \dot x \in A(x)$, when $ A$ is cyclically monotone and upper semi-continuous.


References [Enhancements On Off] (What's this?)

  • [1] Jean-Pierre Aubin and Arrigo Cellina, Differential inclusions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 264, Springer-Verlag, Berlin, 1984. Set-valued maps and viability theory. MR 755330 (85j:49010)
  • [2] H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam, 1973.
  • [3] Kôsaku Yosida, Functional analysis, 6th ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 123, Springer-Verlag, Berlin-New York, 1980. MR 617913 (82i:46002)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0969314-6
PII: S 0002-9939(1989)0969314-6
Article copyright: © Copyright 1989 American Mathematical Society