Abstract
The aim of this paper is to obtain an existence result for impulsive differential inclusions of first order with boundary conditions in Hilbert spaces under a hypothesis of integrability in the Henstock–Lebesgue sense for the multifunction on the right-hand side. The proof is based on the assumption that there exists a solution tube for the inclusion taken under consideration (this novel concept which generalizes the extensively used notions of upper and lower solution was adapted to the present setting). Finally, a compactness property is proved.
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