Diagonalisation method in the asymptotical theory for solutions of systems of ODE

Abstract

The question about asymptotical behaviour of solutions for the system $\dot{x}=A_{\nu }x+f$ for big values of the parameter $\nu \in \mathfrak{A}$ is considered. An approach to the reduction of a large class of problems to easily solvable problem with diagonal coefficient matrix is described. This approach is based on the approximation of summable matrix function $A_{\nu }$ by specially constructed smooth matrix functions.

11 pages, in Russian