Differential equations on closed subsets of a Banach space
1973; American Mathematical Society; Volume: 179; Linguagem: Inglês
10.1090/s0002-9947-1973-0318991-4
ISSN1088-6850
Autores Tópico(s)Nonlinear Differential Equations Analysis
ResumoIn this paper the problem of existence of solutions to the initial value problem u ′ ( t ) = A ( t , u ( t ) ) , u ( a ) = z u’(t) = A(t,u(t)),u(a) = z , is considered where A : [ a , b ) × D → E A:[a,b) \times D \to E is continuous, D is a closed subset of a Banach space E , and z ∈ D 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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