On a majorant–minorant criterion for the total preservation of global solvability of distributed controlled systems

Abstract

For distributed controlled systems that can be represented by a functional-operator equation of the Hammerstein type with an additional term on the right-hand side in the form of a linear operator (an extended equation of the Hammerstein type), we prove a criterion for the total (over the entire set of admissible controls) preservation of global solvability. In this connection, we develop an earlier-proved majorant–minorant criterion for the total preservation of global solvability. As an example, we study a controlled semilinear integro-differential equation describing radiation transport with Compton scattering diagram. The choice of this example is explained, in particular, by the fact that the preceding version of the majorant–minorant criterion is not applicable to it.