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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Counterexample to a theorem on differential equations in Hilbert space


Author: William J. Knight
Journal: Proc. Amer. Math. Soc. 51 (1975), 378-380
MSC: Primary 34G05
DOI: https://doi.org/10.1090/S0002-9939-1975-0372357-7
MathSciNet review: 0372357
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Abstract: A counterexample is given to a theorem by Felix Browder concerning solutions of differential equations with values in Hilbert space. Several valid conclusions (as near the original conclusions as possible) are pointed out.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0372357-7
Keywords: Nonlinear differential equation, Hilbert space, strongly $ {C^1}$-solution, weakly continuous map, weak derivative, Pettis integral, Bochner integral
Article copyright: © Copyright 1975 American Mathematical Society