Generalized green operator of a boundary-value problem with degenerate pulse influence

We establish necessary and sufficient conditions for the solvability of inhomogeneous linear boundaryvalue problems for systems of ordinary differential equations with pulse influence in the case where the number of boundary conditions is not equal to the order of the differential system (Noetherian problems). We construct a generalized Green operator for boundary-value problems not all solutions of which can be extended from the left endpoint to the right endpoint of the interval where these solutions are constructed.