Mykola Hladiy - Generalized Green's operator of boundary value problem with impulse action

We find necessary and suficient conditions for solvability of nonhomogeneous linear boundary value problems for systems of ordinary diferential equations with impulsive force in general case where the number of bounadry value conditions is not equal to the order of the differential systems.

We construct a generalized Green's operator for boundary value problems, not every solutions of which can be extendnfrom left end point to the right end point of the interval where the solution is defined.

A. M. Samoilenco and N. A. Perestyuk, Differential equations with impulsive action. Kyiv: Vyscha shkola, 1987, 287 pages (in Russian).