Generalized Baire category and differential inclusions in Banach spaces (Q1109194)

The authors study the Cauchy problem \(\dot x(t)\in F(x(t))\), \(x(0)=x_ 0\in E\) in a separable reflexive Banach space E where F is a Hausdorff continuous multifunction with closed, bounded values. They prove that this problem has a Carathéodory solution on some interval (0,T) provided the set \(\overline{co}F(x_ 0)\) has finite codimension which means that for some closed affine subspace \(E_ 0\subseteq E\) with finite codimension the set \(E_ 0\cap \overline{co}F(x_ 0)\) has nonempty interior relative to \(E_ 0\).