Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shooting with degree theory: Analysis of some weighted poly-harmonic
  systems   In this paper, the author establishes the existence of positive entire
solutions to a general class of semilinear poly-harmonic systems, which
includes equations and systems of the weighted Hardy--Littlewood--Sobolev type.
The novel method used implements the classical shooting method enhanced by
topological degree theory. The key steps of the method are to first construct a
target map which aims the shooting method and the non-degeneracy conditions
guarantee the continuity of this map. With the continuity of the target map, a
topological argument is used to show the existence of zeros of the target map.
The existence of zeros of the map along with a non-existence theorem for the
corresponding Navier boundary value problem imply the existence of positive
solutions for the class of poly-harmonic systems.

10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat