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On optimal mild solutions of non-homogeneous differential equations in Banach spaces†

Published online by Cambridge University Press:  14 November 2011

S. Zaidman
S. Zaidman
Affiliation:
Départment de Mathématiques et de Statistique, Université de Montréal, Canada
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Synopsis

Consider mild solutions on the real line of non-homogeneous differential equations in a Banach space: u′(t) = Au(t) + f(t), where A is the infinitesimal generator of a C0-semigroup.

We prove an existence result for optimal solutions (as defined in the text) in reflexive spaces and an uniqueness fact in uniformly convex B-spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 3-4 , 1979 , pp. 273 - 277
Copyright
Copyright © Royal Society of Edinburgh 1979

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