Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic formulas for fundamental system of solutions of high order
  ordinary differential equations with coefficients -- distributions   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 $n=2m\geqslant
2$, $\lambda$ is the large complex parameter, the positive functions\
$\varrho$\ and\ $\tau_{0,0}$ \ belong to $W^{1,1}[0,1]$ and the complex valued
coefficients $\tau_{k,s}$ are such that the anti-derivatives
$\tau_{k,s}^{(-l)}$ belong to $L_2[0,1]$, provided that $l=\min\{k,s\}$. Here
the anti-derivatives are understood in the sense of distributions. The above
equation can be reduced to the $n$-th order system of differential equations of
the form $$ \mathbf y'=\lambda\rho(x)\mathrm B\mathbf y+\mathrm A(x)\mathbf
y+\mathrm C(x,\lambda)\mathbf y $$ with constant matrix $\mathrm B$ and
summable matrices $\mathrm A(x)$ and $\mathrm C(x,\lambda)$. The first
objective of the paper is obtain new results on asymptotic representation for
the matrix of fundamental solutions of the last equation with respect to
$\lambda\to\infty$ in certain sectors of the complex plane. The second
objective is to apply the obtained results for analyzing the asymptotic
representation of fundamental solutions of the first scalar equation with
distribution coefficients.

14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th