LAUSR

For control and observation problems considered for operator equations of the first kind in Banach spaces, an controllability criterion is stated. In the case of reflexive strictly convex (B)-spaces, the BUME method and the method of monotone mappings are used to find optimal controls and an abstract maximum principle is formulated. The indicated problems for ODE systems in $${{\mathbb{R}}^{n}}$$ are investigated as an example.