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Existence and Topological Properties of Solution Sets for Differential Inclusions with Delay

100%

Gomaa A. M.

Commentationes Mathematicae

2008

tom 48

nr 1

We consider the problem \(\dot{x}(t) \in A(t)x(t) + F (t, θ_t x))\) a.e. on \([0, b]\), \(x = \kappa\) on \([-d, 0]\) in a Banach space \(E\), where \(\kappa\) belongs to the Banach space, \(C_E ([-d, 0])\), of all continuous functions from \([-d, 0]\) into \(E\). A multifunction \(F\) from \([0, b] \times C_E ([-d, 0])\) into the set, \(P_{f_c} (E)\), of all nonempty closed convex subsets of \(E\) is weakly sequentially hemi-continuous, \(θ_t x(s) = x(t + s)\) for all \(s \in [-d, 0]\) and \(\{A(t) : 0 \leq t \leq b\}\) is a family of densely defined closed linear operators generating a continuous evolution operator \(S(t, s)\). Under a generalization of the compactness assumptions, we prove an existence result and give some topological properties of our solution sets that generalizes earlier theorems by Papageorgiou, Rolewicz, Deimling, Frankowska and Cichoń.

Delay perturbed evolution problems involving time dependent subdifferential operators

75%

Saïdi S., Yarou M.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2014

tom 34

nr 1

61-87

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.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Gomaa A. M.

1 Saïdi S.

1 Yarou M.

1 2014

1 2008

Wyniki wyszukiwania

Existence and Topological Properties of Solution Sets for Differential Inclusions with Delay

Delay perturbed evolution problems involving time dependent subdifferential operators