Polynomial quasi-solutions to linear systems of difference-differential equations (Q1589122)

Here, the following delay differential equation is investigated \[ \ddot x(t)= A(t) x(t- 1)+ f(t),\quad t\in\mathbb{R},\quad x(0)= x_0, \] where \(A(t)\) is a polynomial matrix function and \(f(t)\) is a polynomial vector function. Under certain conditions it is proved that the problem has a unique polynomial solution. Some examples are considered.