Malkhaz Ashordia ON THE SOLVABILITY OF THE PERIODIC TYPE BOUNDARY VALUE PROBLEM FOR LINEAR SYSTEMS OF GENERALIZED ORDINARY DIFFERENTIAL EQUATIONS

Let ω be a positive number. For the linear system of generalized ordinary differential equations dx(t) = dA(t) · x(t) + df(t) for t ∈ R (1) we investigate the periodic boundary value problem x(t + ω) = x(t) for t ∈ R, (2) where A = (aik) n i,k=1 : R → R n×n and f = (fi) n i=1 : R → R n are, respectively, matrixand vector-functions with bounded total variation components on the closed interval [0, ω], and A(t + ω) = A(t) + A(ω) for t ∈ R (3) and f(t + ω) = f(t) + f(ω) for t ∈ R. (4) Note that the following ω-type boundary value problem x(t + ω) = x(t) + c for t ∈ R,