Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The floating-body problem: an integro-differential equation without
  irregular frequencies   The linear boundary value problem under consideration describes time-harmonic
motion of water in a horizontal three-dimensional layer of constant depth in
the presence of an obstacle adjacent to the upper side of the layer (floating
body). This problem for a complex-valued harmonic function involves mixed
boundary conditions and a radiation condition at infinity. Under rather general
geometric assumptions the existence of a unique solution is proved for all
values of the nonnegative problem's parameter related to the frequency of
oscillations. The proof is based on the representation of solution as a sum of
simple- and double-layer potentials with densities distributed over the
obstacle's surface, thus reducing the problem to an indefinite
integro-differential equation. The latter is shown to be soluble for all
continuous right-hand side terms for which purpose S.~G. Krein's theorem about
indefinite equations is used.

0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga