Existence, uniqueness and closed form solutions for boundary value matrix problems (Q1103085)

This paper concerns with boundary value problems for the second order matrix differential equation \(X^{(2)}(t)+A_ 1X^{(1)}(t)+A_ 0X(t)=F(t).\) In an analogous way to the scalar case, we represent the general solution of this equation in terms of an appropriate pair of solutions of the algebraic matrix equation \(X^ 2+A_ 1X+A_ 0=0.\) Thus existence and uniqueness conditions for solutions of boundary value differential problems related to the equation as well as explicit and computable expressions for solutions are given.