Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-classical states for the Nonlinear Schr\"odinger Equation on saddle
  points of the potential via variational methods   In this paper we study semiclassical states for the problem $$ -\eps^2 \Delta
u + V(x) u = f(u) \qquad \hbox{in} \RN,$$ where $f(u)$ is a superlinear
nonlinear term. Under our hypotheses on $f$ a Lyapunov-Schmidt reduction is not
possible. We use variational methods to prove the existence of spikes around
saddle points of the potential $V(x)$.

18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
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The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph