Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Exhaustive existence and non-existence results for some prototype
  polyharmonic equations in the whole space
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat