无穷维空间中微分包含可达集的唯一性

THE UNIQUENESS OF THE REACHABLE SET OF DIFFERENTIAL INCLUSIONS IN INFINITE DIMENSIONAL SPACE

在可分Ｂａｎａｃｈ空间Ｘ中考虑下列微分包含的可达集ｘ（ｔ）∈Ｆ（ｔ，ｘ（ｔ）），ａ．ｅ．ｔ∈［ｔ０，Ｔ］ｘ（ｔ０）＝ξ｛其中Ｆ是从［ｔ０，Ｔ］×Ｘ到Ｘ的取紧凸值的非空集值映射．给出了有关可达集的一些性质，并且利用有关可达集的集值映射ｔ～→Ｒ（ｔ０，ｔ；ξ）关于ｔ的半群性质，证明了可达集的唯一性．其中Ｒ（ｔ０，ｔ；

In this paper, we study the reachable set of the following differential inclusion in separatedble Banach space X x ·(t)∈F(t,x(t)), a.e.t∈ t 0,T x(t 0)=ξ where F is a set valued map from t 0,T ×X to X with nonempty compact convex values. We obtain some properties of the reachable set, and prove the uniqueness of the reachable set in terms of the semigroup properties in t of the set valued map t ￣→R(t 0,t;ξ), where R(t 0,t;ξ) is the reachable set of differential inclusions.