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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Fundamental theory of contingent differential equations in Banach space


Authors: Shui Nee Chow and J. D. Schuur
Journal: Trans. Amer. Math. Soc. 179 (1973), 133-144
MSC: Primary 34G05; Secondary 47H15
MathSciNet review: 0324162
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Abstract: For a contingent differential equation that takes values in the closed, convex, nonempty subsets of a Banach space E, we prove an existence theorem and we investigate the extendability of solutions and the closedness and continuity properties of solution funnels. We consider first a space E that is separable and reflexive and then a space E with a separable second dual space. We also consider the special case of a point-valued or ordinary differential equation.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0324162-8
Keywords: Ordinary differential equations, contingent differential equations, existence of solutions, fundamental theory, Banach spaces, weak topology, upper semicontinuity
Article copyright: © Copyright 1973 American Mathematical Society