Viability theory and fuzzy differential equations

New results are presented which guarantee the existence of viable solutions to differential inclusions. We show that a viable solution exists if (i) a tangency condition is satisfied, and (ii) there exists a maximal solution to an appropriate differential equation. In addition, we discuss the topological structure of the solution set. These results will then be used with the stacking theorem to establish new existence criteria for fuzzy differential equations if there exists a maximal solution for an appropriate set of differential equations.