On difference differential equations with periodic coefficients

where x(t) is the vector of solution and A(t) is a matrix with continuous periodic elements. It signifies that each solution of (1.1) is a linear combination of n particular solutions, the components of which are of the form t* exp at/o p(t), P.2) p(t) being a periodic function of period co, ea being a root of a certain algebraic equation of degree IZ, and Y is a nonnegative integer which can be different from zero only in case the corresponding number em is a multiple root. The “characteristic equation” may be written explicitly in the form det (zf -Q,“(A)) = 0