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Periodic solutions of evolution problem associated with moving convex sets

100%

Castaing C., Monteiro Marques M.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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1995

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tom 15

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nr 2

99-127

EN

This paper is concerned with periodic solutions for perturbations of the sweeping process introduced by J.J. Moreau in 1971. The perturbed equation has the form $-Du ∈ N_{C(t)}(u(t)) + f(t,u(t))$ where C is a T-periodic multifunction from [0,T] into the set of nonempty convex weakly compact subsets of a separable Hilbert space H, $N_{C(t)}(u(t))$ is the normal cone of C(t) at u(t), f:[0,T] × H∪H is a Carathéodory function and Du is the differential measure of the periodic BV solution u. Several existence results of periodic solutions for this differential inclusion are stated under various assumptions on the moving convex set C(t) and the perturbation f.

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Convergence results for a class of pramarts and superpramarts in Banach spaces

100%

Castaing C., Salvadori A.

Commentationes Mathematicae

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2013

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tom 53

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nr 2

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Convergence of conditional expectations for unbounded closed convex random sets

81%

Castaing C., Ezzaki F., Hess C.

Studia Mathematica

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1997

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tom 124

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nr 2

133-148

EN

We discuss here several types of convergence of conditional expectations for unbounded closed convex random sets of the form $E^{ℬ_n}X_n$ where $(ℬ_n)$ is a decreasing sequence of sub-σ-algebras and $(X_n)$ is a sequence of closed convex random sets in a separable Banach space.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Studia Mathematica

3 Castaing C.

1 Ezzaki F.

1 Hess C.

1 Monteiro Marques M.

1 Salvadori A.

1 2013

1 1997

1 1995

Periodic solutions of evolution problem associated with moving convex sets

Convergence results for a class of pramarts and superpramarts in Banach spaces

Convergence of conditional expectations for unbounded closed convex random sets