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

• Autorzy: Adel Mahmoud Gomaa
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Differential inclusions; mutifunctions; measures of noncompactness; delay

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2008
• Tom: 48
• Numer: 1

Daty

wydano

2008

online

2017-12-19

Twórcy

autor

Adel Mahmoud Gomaa

Identyfikatory

DOI

10.14708/cm.v48i1.5258