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On functional differential inclusions in Hilbert spaces

100%

Aitalioubrahim M.

tom 32

nr 1

63-85

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.

Second-Order Viability Problem: A Baire Category Approach

63%

Aitalioubrahim M. , Sajid S.

Bulletin of the Polish Academy of Sciences. Mathematics

2009

tom 57

nr 1

9-23

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.

Second-order viability result in Banach spaces

63%

Aitalioubrahim M. , Sajid S.

tom 30

nr 1

5-21

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.