Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic solutions for the one-dimensional fractional Laplacian   In this paper we are concerned with the construction of periodic solutions of
the nonlocal problem $(-\Delta)^s u= f(u)$ in $\mathbb{R}$, where $(-\Delta)^s$
stands for the $s$-Laplacian, $s\in (0,1)$. We introduce a suitable framework
which allows to reduce the search for such solutions to the resolution of a
boundary value problem in a suitable Hilbert space, thereby making it possible
to reach for the usual tools of nonlinear analysis, like bifurcation theory or
variational methods. We obtain some existence theorems which are lately
enlightened with the analysis of some examples.

7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat