Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the conditions of the solvability of boundary value problems for a
  single high-order equation with variable coefficients   A Dirichlet-type problem is studied for an equation of even order with
variable coefficients. A criterion for the uniqueness of a solution is given.
The solution is built in the form of a Fourier series. When justifying the
convergence of the series, the problem of small denominators arises. Sufficient
conditions for the separability of the denominator from zero are obtained. It
is shown that the solvability of the problem is influenced not only by the
dimension of the rectangle, but also by the orders of the specified derivatives
at the lower boundary of the rectangle.

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an