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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.

On fourth-order boundary-value problems

Myelkebir Aitalioubrahim — 2010

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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.

Second-order viability result in Banach spaces

Myelkebir AitalioubrahimSaid Sajid — 2010

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

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