Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stationary solutions of the nonlinear Schr\"odinger equation with
  fast-decay potentials concentrating around local maxima   We study positive bound states for the equation $$- \epsilon^2 \Delta u + Vu
= u^p, \qquad \text{in $\mathbf{R}^N$}, $$ where $\epsilon > 0$ is a real
parameter, $\frac{N}{N-2} < p < \frac{N+2}{N-2}$ and $V$ is a nonnegative
potential. Using purely variational techniques, we find solutions which
concentrate at local maxima of the potential $V$ without any restriction on the
potential.

12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol