The variational stability of an optimal control problem for Volterra-type equations

We study the variational stability of an optimal control problem for a Volterra-type nonlinear functional-operator equation. This means that for this optimal control problem ($P_\varepsilon$) with a parameter $\varepsilon$ we study how its minimum value $\min(P_\varepsilon)$ and its set of minimizers $\operatorname{argmin}(P_\varepsilon)$ depend on $\varepsilon$. We illustrate the use of the variational stability theorem with a series of particular problems.