A viability result for a first-order differential inclusion (Q2492139)

The authors investigated the mobility of a given set \(k\subset\mathbb{R}^n\) for the differential inclusion \[ x'(t)\in f(t,x)+ F(x), \] where \(f\) is single-valued Carathéodory and \(F\) is upper semicontinuous with compact values. The viability result is well-known when \(F\) is furthermore convex valued. Here the authors generalize this assumption assuming that \[ F(x)\in\partial V(x), \] where \(V\) is convex proper. They obtain a new viability result under this assumption.