Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional diffusion with Neumann boundary conditions: the logistic
  equation   Motivated by experimental studies on the anomalous diffusion of biological
populations, we introduce a nonlocal differential operator which can be
interpreted as the spectral square root of the Laplacian in bounded domains
with Neumann homogeneous boundary conditions. Moreover, we study related linear
and nonlinear problems exploiting a local realization of such operator as
performed in [X. Cabre' and J. Tan. Positive solutions of nonlinear problems
involving the square root of the Laplacian. Adv. Math. 2010] for Dirichlet
homogeneous data. In particular we tackle a class of nonautonomous
nonlinearities of logistic type, proving some existence and uniqueness results
for positive solutions by means of variational methods and bifurcation theory.

9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc