Existence of solutions for parabolic-type evolution differential inclusions and properties of the solution set (Q1307984)

The purpose of this paper is to study the parabolic-type differential inclusion with the operator \(A\) depending on time \(t\) in Banach spaces \[ x'(t)+A(t)x(t)\in F(t,x(t)),\quad \text{a.e.}\quad t\in I,\quad x(0)=x_0.\tag{1} \] An existence theorem to problem (1) with convex right-hand sides is proved and properties of the solution set are given. Some results by \textit{J.-P. Aubin} and \textit{A. Cellina} [Differential Inclusions. Set-valued maps and viability theory, Berlin, Springer-Verlag (1984; Zbl 0538.34007)] are used in the proofs.