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Remarques sur la structure interne des composantes connexes semi-Fredholm

100%

Mbekhta M.

Studia Mathematica

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1994

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tom 110

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nr 3

251-256

FR

Soit C(X,Y) l'ensemble des opérateurs fermés à domaines denses dans l'espace de Banach X à valeurs dans l'espace de Banach Y, muni de la métrique du gap. Soit $F_n = {T ∈ C(X,Y): T semi-Fredholm avec ind(T) = n}$ et $C_{n,m} = {T ∈ F_n : α(T) = n + m}$, où α (T) est la dimension du noyau de T. Nous montrons que $⋃^{j}_{m = 0} C_{n,m}$ est un ouvert de $F_n$ (et donc ouvert dans C(X,Y)) et que $C_{n,m}$ est dense dans $⋃_{j≥m} C_{n,j}$. Nous déduisons quelques résultats de densités. A la fin de se travail nous donnons un exemple d'espace de Banach X tel que, d'une part, $F_n$ n'est pas connexe dans B(X) et d'autre part, l'ensemble des opérateurs semi-Fredholm n'est pas dense dans B(X), contrairement au cas Hilbertien.

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Delay perturbed evolution problems involving time dependent subdifferential operators

75%

Saïdi S., Yarou M.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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2014

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tom 34

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nr 1

61-87

EN

We investigate in the present paper, the existence and uniqueness of solutions for functional differential inclusions involving a subdifferential operator in the infinite dimensional setting. The perturbation which contains the delay is single-valued, separately measurable, and separately Lipschitz. We prove, without any compactness condition, that the problem has one and only one solution.

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Periodic solutions of evolution problem associated with moving convex sets

75%

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.

Ograniczanie wyników

2 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Studia Mathematica

1 Castaing C.

1 Mbekhta M.

1 Monteiro Marques M.

1 Saïdi S.

1 Yarou M.

1 2014

1 1995

1 1994

Remarques sur la structure interne des composantes connexes semi-Fredholm

Delay perturbed evolution problems involving time dependent subdifferential operators

Periodic solutions of evolution problem associated with moving convex sets