Geodesic
On functional differential inclusions in Hilbert spaces
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 32 (2012) no. 1, pp. 63-85

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We prove the existence of monotone solutions, of the functional differential inclusion ẋ(t) ∈ f(t,T(t)x) +F(T(t)x) in a Hilbert space, where f is a Carathéodory single-valued mapping and F is an upper semicontinuous set-valued mapping with compact values contained in the Clarke subdifferential ∂_c V(x) of a uniformly regular function V.
Keywords: functional differential inclusion, regularity, Clarke subdifferential 
Aitalioubrahim, Myelkebir. On functional differential inclusions in Hilbert spaces. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 32 (2012) no. 1, pp. 63-85. http://geodesic.mathdoc.fr/item/DMDICO_2012_32_1_a2/
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