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 ${\partial}_{c}V\left(x\right)$ of a uniformly regular function V.

We show the existence of solutions to a boundary-value problem for fourth-order differential inclusions in a Banach space, under Lipschitz’s contractive conditions, Carathéodory conditions and lower semicontinuity conditions.

We prove a theorem on the existence of solutions of a first order functional differential inclusion governed by a class of nonconvex sweeping process with a noncompact perturbation.

We show the existence result of viable solutions to the second-order differential inclusion
ẍ(t) ∈ F(t,x(t),ẋ(t)),
x(0) = x₀, ẋ(0) = y₀, x(t) ∈ K on [0,T],
where K is a closed subset of a separable Banach space E and F(·,·,·) is a closed multifunction, integrably bounded, measurable with respect to the first argument and Lipschitz continuous with respect to the third argument.

The paper deals with the existence of viable solutions to the differential inclusion
ẍ(t) ∈ f(t,x(t)) + ext F(t,x(t)),
where f is a single-valued map and ext F(t,x) stands for the extreme points of a continuous, convex and noncompact set-valued mapping F with nonempty interior.

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