On the set of solutions to a class of nonconvex nonclosed differential inclusions (Q1271938)

The arcwise connectedness of the solution set to the Cauchy problem for differential inclusions with multivalued control constraint \[ \dot{x} \in F(t,x,G(t,x)), \quad x(0) = \xi, \] \((F : [0,a]\times X\times Y \rightarrow 2^{X}\), \(G : [0,a]\times X \rightarrow 2^{Y}; X, Y \) are Banach spaces) is shown under the Lipschitz condition on the multivalued functions \(F, G\) and the contractedness of \(F\) with respect to the third variable. The solvability of the periodic problem \(x(0) = x(a)\), and of the problem \( x(0) \in D_{0}\), \(x(a) \in D_{a}\) (\(D_{0}, D_{a}\) are closed subsets of \(X\)) is proved for the above inclusions.