Abstract
We prove the existence result of monotone solutions, in Hilbert space, for the differential inclusion ẍ(t) ∈ f (t,T (t)x, ẋ(t))+F(T (t)x, ẋ(t)) , where f is a Caratheodory single-valued mapping and F is an upper semicontinuous set-valued mapping with compact values contained in the Clarke subdifferential ∂cV(x) of a uniformly regular function V. Mathematics subject classification (2010): 34A60, 34K05, 34K25.
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