In this chapter we shall carry out a detailed investigation of some particular cases of the general optimization problems which were discussed in Chapter IV. Namely, we shall study the case where the operator equations*x*=*Tx*with*T*∈*W*represent ordinary differential equations with a so-called control variable.

1 More precisely, we shall concern ourselves with problems which are defined in terms of some given*n*-vector-valued function*f*, whose domain is G ×*V*×*I*, where G is a given open set in*R ^{n}*,