Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple solutions to singular fourth order elliptic equations   Using the method of Nehari manifold, we prove the existence of at least two
distinct weak solutions to elliptic equation of four order with singulatities
and with critical Sobolev growth.

4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph