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

 

Strong solutions of evolution equations governed by $ m$-accretive operators and the Radon-Nikodým property


Author: Robert Deville
Journal: Proc. Amer. Math. Soc. 112 (1991), 1001-1008
MSC: Primary 47H15; Secondary 34G20, 47H06, 47H20
MathSciNet review: 1045133
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Abstract: We construct, in every Banach space which fails the Radon-Nikodym property, a nonlinear operator $ A$ which is $ m$-accretive for some equivalent norm in $ X$, such that the domain of $ A$ is not a singleton and such that the only strong solutions of the equation $ u' + Au \mathrel\backepsilon f$ are the constant ones.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1045133-9
PII: S 0002-9939(1991)1045133-9
Keywords: $ m$-accretive operators, nonlinear evolution equations, Radon-Nikodym property, strong solutions
Article copyright: © Copyright 1991 American Mathematical Society