Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Liouville theorem for indefinite fractional diffusion equations and
  its application to existence of solutions   In this work we obtain a Liouville theorem for positive, bounded solutions of
the equation $$ (-\Delta)^s u= h(x_N)f(u) \quad \hbox{in }\mathbb{R}^{N} $$
where $(-\Delta)^s$ stands for the fractional Laplacian with $s\in (0,1)$, and
the functions $h$ and $f$ are nondecreasing. The main feature is that the
function $h$ changes sign in $\mathbb{R}$, therefore the problem is sometimes
termed as indefinite. As an application we obtain a priori bounds for positive
solutions of some boundary value problems, which give existence of such
solutions by means of bifurcation methods.

15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph