Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and instability of deformed catenoidal solutions for
  fractional Allen--Cahn equation   We develop a new infinite dimensional gluing method for fractional elliptic
equations. As a model problem, we construct solutions of the fractional
Allen--Cahn equation vanishing on a rotationally symmetric surface which
resembles a catenoid and have sub-linear growth at infinity. Moreover, such
solutions are unstable.

8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph