  We investigate full Lipschitzian and full H\"olderian stability for a class
of control problems governed by semilinear elliptic partial differential
equations, where all the cost functional, the state equation, and the
admissible control set of the control problems undergo perturbations. We
establish explicit characterizations of both Lipschitzian and H\"olderian full
stability for the class of control problems. We show that for this class of
control problems the two full stability properties are equivalent. In
particular, the two properties are always equivalent in general when the
admissible control set is an arbitrary fixed nonempty, closed, and convex set.
