On the existence of solutions to differential equations remaining in a given closed set (Q2765903)

Differential inclusions on closed subsets of the Euclidean space \(\mathbb{R}^n\) are studied. Several interesting results devoted to the existence of solutions remaining in a considered closed subset of \(\mathbb{R}^n\) are presented. Sufficient conditions are expressed in topological terms, i.e., under the assumption that the considered closed set is a strong deformation retract or under homological conditions on it.