Existence theorem for weak solutions to random differential inclusions in Banach spaces (Q2767453)

The authors consider a Cauchy problem for differential inclusions of the type \(x'(t) \in F(t,x(t))\), a.e. on \([a,b]\), \(x(a)=x_0\), where \(F\) is a set-valued map with values in a real reflexive Banach space. On this problem the authors give an existence result for weak solutions when \(F\) is controlled by a weakly integrable bounded set-valued map. In the second part, a random differential inclusion is examined, and the existence of weak solutions is proved for it.