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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 adesired control $u_d$. It is proved that such problems are always nonuniquelysolvable for certain choices of the tuple $(y_d, u_d)$ and instable in thesense that the set of solutions (interpreted as a multivalued function of$(y_d, u_d)$) does not admit a continuous selection.

On the Nonuniqueness and Instability of Solutions of Tracking-Type Optimal Control Problems