Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existece and multiplicity results for nonlinear critical Neumann problem
  on compact manifolds   we study on compact Riemannian manifolds with boundary, the problems of
existence and multiplicity of solutions to a Neumann problem involving the
p-Laplacian operator and critical Sobolev exponents.

15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th