Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple Solutions for Scalar Field Equations with Potentials having
  "Subsidences"   In this paper the question of finding infinitely many solutions to the
problem $-\Delta u+a(x)u=|u|^{p-2}u$, in $\mathbb{R}^N$, $u \in
H^1(\mathbb{R}^N)$, is considered when $N\geq 2$, $p \in (2, 2N/(N-2))$, and
the potential $a(x)$ is a positive function which is not required to enjoy
symmetry properties. Assuming that $a(x)$ satisfies a suitable "slow decay at
infinity" condition and, moreover, that its graph has some "dips", we prove
that the problem admits either infinitely many nodal solutions either
infinitely many constant sign solutions. The proof method is purely variational
and allows to describe the shape of the solutions.

23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs