Boundary value problem for system of finite-difference with averaging equations
The boundary value problem for the system of linear nonhomogeneous differential equations with generalized coefficients is considered X(t) = L(t)X(t) + F(t), M1X(0) + M2X(b) = Q, where t ∈ T = [0, b], L : T → Rpxp and F : T → Rp are right-continuous matrix and vector valued functions of bounded variation; M1, M2 ∈ Rpxp, Q ∈ Rp are defined matrices and vector. The problem is investigated with the help of the corresponding finite-difference with averaging equation behavior studying. The definition of the fundamental matrix, corresponding to the finite-difference with averaging equation is introduced. The theorem of the existence and uniqueness of the finite-difference with averaging boundary value problem, corresponding to the described system is proved.