Solution of the Cauchy problem for two descriptive equations with Fredholm operator (Q2353031)

The initial value problem for equations in a Banach space with a noninvertible operator multiplying the derivative and under the sign of differentiation is solved. Solutions for inhomogeneous equations in the cases of unique and nonunique solvability are obtained. A comparison of solutions is performed. The importance of the problems under consideration follows from the practical need for determination of the complete controllability properties of dynamical systems unresolved with respect to the derivative. It was proved that the regular considered systems are or are not completely controllable simultaneously.