Differential Equations on Closed Subsets of a Banach Space
Open Access
- 1 May 1973
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 179, 399-414
- https://doi.org/10.2307/1996511
Abstract
In this paper the problem of existence of solutions to the initial value problem <!-- MATH $u'(t) = A(t,u(t)),u(a) = z$ --> , is considered where <!-- MATH $A:[a,b) \times D \to E$ --> is continuous, D is a closed subset of a Banach space E, and . 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.
Keywords
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