Differential equations on closed subsets of a Banach space

Martin, R. H.

doi:10.1090/S0002-9947-1973-0318991-4

Differential equations on closed subsets of a Banach space
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Trans. Amer. Math. Soc. 179 (1973), 399-414 Request permission

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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