Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian elliptic systems: a guide to variational frameworks   Consider a Hamiltonian system of type \[ -\Delta u=H_{v}(u,v),\ -\Delta
v=H_{u}(u,v) \ \ \text{ in } \Omega, \qquad u,v=0 \text{ on } \partial \Omega
\] where $H$ is a power-type nonlinearity, for instance $H(u,v)=
|u|^p/p+|v|^q/q$, having subcritical growth, and $\Omega$ is a bounded domain
of $\mathbb{R}^N$, $N\geq 1$. The aim of this paper is to give an overview of
the several variational frameworks that can be used to treat such a system.
Within each approach, we address existence of solutions, and in particular of
ground state solutions. Some of the available frameworks are more adequate to
derive certain qualitative properties; we illustrate this in the second half of
this survey, where we also review some of the most recent literature dealing
mainly with symmetry, concentration, and multiplicity results. This paper
contains some original results as well as new proofs and approaches to known
facts.

28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex