Asymptotics of Solutions to Differential Equations near Singular Points

Conditions are obtained under which all solutions to a normal system of equations asymptotically or strongly asymptotically approximate to polynomials as the argument tends to infinity. For the system of the form $L\mathbf x=\mathbf f$, where $L$ is a first-order linear differential operator, conditions are found under which all its solutions $L$-asymptotically approximate to the solutions of the homogeneous system $L\mathbf x=\mathbf 0$ as the argument tends to the singular point of the former system.