A multipoint boundary value problem for systems of linear generalized differential equations with singularities

We study a multipoint boundary value problem for systems of Kurzweil generalized linear differential equations with singularities on a finite closed interval of the real line. We assume that the offdiagonal entries of the matrix function corresponding to the system, as well as the elements of the right-hand side of the system, have bounded variation on the entire interval; however, the diagonal entries of the matrix function are not assumed to have bounded variation on the entire interval. This is what we mean by saying that the system is singular. We study the unique solvability of the problem. We prove a general theorem and use it to we obtain efficient optimal (in particular, spectral) solvability conditions for the problem.