Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On doubly nonlocal fractional elliptic equations   This work is devoted to the study of the existence of solutions to nonlocal
equations involving the fractional Laplacian. These equations have a
variational structure and we find a nontrivial solution for them using the
Mountain Pass Theorem. To make the nonlinear methods work, some careful
analysis of the fractional spaces involved is necessary. In addition, we
require rather general assumptions on the local operator. As far as we know,
this result is new and represent a fractional version of a classical theorem
obtained working with Laplacian equations.

21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph