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This paper deals with differential equations of the form $$ \tau(y)- \lambda^{2m} \varrho(x) y = 0, \quad \tau(y)=\sum_{k,\,s=0}^m(\tau_{k,\,s}(x)y^{(m-k)}(x))^{(m-s)}, $$ where $n=2m\geqslant2$, $\lambda$ is the large complex parameter, the positive functions\$\varrho$\ and\ $\tau_{0,0}$ \ belong to $W^{1,1}[0,1]$ and the complex valuedcoefficients $\tau_{k,s}$ are such that the anti-derivatives$\tau_{k,s}^{(-l)}$ belong to $L_2[0,1]$, provided that $l=\min\{k,s\}$. Herethe anti-derivatives are understood in the sense of distributions. The aboveequation can be reduced to the $n$-th order system of differential equations ofthe form $$ \mathbf y'=\lambda\rho(x)\mathrm B\mathbf y+\mathrm A(x)\mathbfy+\mathrm C(x,\lambda)\mathbf y $$ with constant matrix $\mathrm B$ andsummable matrices $\mathrm A(x)$ and $\mathrm C(x,\lambda)$. The firstobjective of the paper is obtain new results on asymptotic representation forthe matrix of fundamental solutions of the last equation with respect to$\lambda\to\infty$ in certain sectors of the complex plane. The secondobjective is to apply the obtained results for analyzing the asymptoticrepresentation of fundamental solutions of the first scalar equation withdistribution coefficients.

Asymptotic formulas for fundamental system of solutions of high order ordinary differential equations with coefficients -- distributions