  We study tracking-type optimal control problems that involve a non-affine,
weak-to-weak continuous control-to-state mapping, a desired state $y_d$, and a
desired control $u_d$. It is proved that such problems are always nonuniquely
solvable for certain choices of the tuple $(y_d, u_d)$ and instable in the
sense that the set of solutions (interpreted as a multivalued function of
$(y_d, u_d)$) does not admit a continuous selection.
