Viability theory applied to discontinuous ordinary differential equations

In this paper we collect some concepts about viability theory that we can use in order to obtain some results for the existence of solutions (and, in many cases, extremal solutions) of discontinuous differential equations. Concretely, we show in this way some results for initial value problems, given in [1], functional value problems, given in [2], and we also give a new result for impulsive problems.