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Transactions of the American Mathematical Society

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



Differential equations on closed subsets of a Banach space

Author: R. H. Martin
Journal: Trans. Amer. Math. Soc. 179 (1973), 399-414
MSC: Primary 47H15; Secondary 34G05
MathSciNet review: 0318991
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Abstract: In this paper the problem of existence of solutions to the initial value problem $ u'(t) = A(t,u(t)),u(a) = z$, is considered where $ A:[a,b) \times D \to E$ is continuous, D is a closed subset of a Banach space E, and $ z \in D$. With a dissipative type condition on A, we establish sufficient conditions for this initial value problem to have a solution. Using these results, we are able to characterize all continuous functions which are generators of nonlinear semigroups on D.

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Keywords: Banach space, nonlinear differential equation, dissipative, nonlinear semigroup
Article copyright: © Copyright 1973 American Mathematical Society