The asymptotic behavior of solutions to linear ordinary differential systems with a parameter on the half-axis

摘要

The study of the asymptotic behavior of solutions to systems of differential equations go back to classical works of Birkhoff, Tamarkin, Perron, and other authors[1–4]. In this paper, we study the linear system (1) with integrable coefficients depending on a parameter on the halfaxis. We suggest a double asymptotics formula both with respect to the parameter and with respect to the argument x. The results generalize those of [3, 4].