Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positive and sign-changing clusters around saddle points of the
  potential for nonlinear elliptic problems   We study the existence of positive and sign-changing multipeak solutions for
the stationary Nonlinear Schroedinger Equation. Here no symmetry on $V$ is
assumed. It is known that this equation has positive multipeak solutions with
all peaks approaching a local maximum of the potential. It is also proved that
solutions alternating positive and negative spikes exist in the case of a
minima. The aim of this paper is to show the existence of both positive and
sign-changing multipeak solutions around a nondegenerate saddle point of the
external potential.

35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
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The categories of this paper are: supr-con
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex