Abstract
In this work, we find necessary and sufficient conditions in order that a family of sets {C(t), t ∈ J} be invariant for a Cauchy problem. We prove the existence and uniqueness of the solution using viability for timedependent closed convex sets to the case of non densely defined Cauchy problem. Moreover, we propose several characterizations of conditions that lead to the viability theorem. Finally, a comparison principle for semilinear problems, when the nonlinear part is only defined in a closed convex set, is established.