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Viability theorems for a class of differential-operator inclusions. (English) Zbl 0694.34011
Discussed in this paper is the following differential inclusion $x'(t)+Ax(t)\in F(x(t))\quad x(0)=x_ 0\in K,\quad x(t)\in K\quad \forall t\geq 0$ where K is compact in a Banach space X, A is the infinitesimal generator of a compact differential semigroup of bounded linear operators, and $$F: K\to 2^ x\setminus \emptyset$$ is upper semicontinuous with compact convex values. It is shown that a natural tangential condition is necessary and sufficient for the existence of a global solution to this problem.
Reviewer: S.Hu

##### MSC:
 34A60 Ordinary differential inclusions 47E05 General theory of ordinary differential operators
##### Keywords:
viability; differential inclusion; global solution
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##### References:
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