Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sublevel sets and global minima of coercive functionals and local minima
  of their perturbations   The aim of the present paper is essentially to prove that if $\Phi$ and
$\Psi$ are two sequentially weakly lower semicontinuous functionals on a
reflexive real Banach space and if $\Psi$ is also continuous and coercive, then
then following conclusion holds: if, for some $r > \inf_X \Psi$, the weak
closure of the set $\Psi^{-1}(]-\infty, r[)$ has at least $k$ connected
components in the weak topology, then, for each $\lambda > 0$ small enough, the
functional $\Psi + \lambda\Phi$ has at least $k$ local minima lying in
$\Psi^{-1}(]-\infty, r[)$.

32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat