  We study linear-quadratic optimal control problems for Voterra systems, and
problems that are linear-quadratic in the control but generally nonlinear in
the state. In the case of linear-quadratic Volterra control, we obtain sharp
necessary and sufficient conditions for optimality. For problems that are
linear-quadratic in the control only, we obtain a novel form of necessary
conditions in the form of double Volterra equation; we prove the solvability of
such equations.
