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On first order impulsive semilinear functional differential inclusions

Mouffak Benchohra, Johnny Henderson, Sotiris K. Ntouyas (2003)

Archivum Mathematicum

In this paper the Leray-Schauder nonlinear alternative for multivalued maps combined with the semigroup theory is used to investigate the existence of mild solutions for first order impulsive semilinear functional differential inclusions in Banach spaces.

On functional differential inclusions in Hilbert spaces

Myelkebir Aitalioubrahim (2012)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

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