On the controllability of a class of differential inclusions depending on a parameter (Q1122137)

We deal with the following stability problem: given a differential inclusion of the form \(x'\in F(t,x,\lambda)\), where \(\lambda\) is a parameter varying in a topological space \(\Lambda\), find conditions under which the set of all \(\lambda\in \Lambda\), such that the differential inclusion is controllable, is open in \(\Lambda\). Applying the author's Theorem 3.1 from ``Differential inclusions depending on a parameter'' [Bull. Polish. Acad. Sci., Dept. Math., (to appear)], we get a result in this direction, assuming, as leader hypotheses, that F(t,\(\cdot,\lambda)\) is a convex process, from \({\mathbb{R}}^ n\) into itself, and that F(t,x,\(\cdot)\) is lower semicontinuous.