Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Schr\"odinger equations without compatibility conditions on
  the potentials   We study the existence of nonnegative solutions (and ground states) to the
nonlinear Schr\"{o}dinger equation in $\mathbb{R}^N$ with radial potentials and
super-linear or sub-linear nonlinearities. The potentials satisfy power type
estimates at the origin and at infinity, but no compatibility condition is
required on their growth (or decay) rates at zero and infinity. In this respect
our results extend some well known results in the literature and we also
believe that they can highlight the role of the sum of Lebesgue spaces in
studying nonlinear equations with weights.

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The categories of this paper are: stat
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio