Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behavior of solutions of semilinear elliptic equations in
  unbounded domains: two approaches   In this paper, we study the asymptotic behavior as $x_1\to+\infty$ of
solutions of semilinear elliptic equations in quarter- or half-spaces, for
which the value at $x_1=0$ is given. We prove the uniqueness and characterize
the one-dimensional or constant profile of the solutions at infinity. To do so,
we use two different approaches. The first one is a pure PDE approach and it is
based on the maximum principle, the sliding method and some new Liouville type
results for elliptic equations in the half-space or in the whole
space~$\mathbb{R}^N$. The second one is based on the theory of dynamical
systems.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom