Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic profiles for a nonlinear Schr\"odinger equation with critical
  combined powers nonlinearity   We study asymptotic behaviour of positive ground state solutions of the
nonlinear Schr\"odinger equation $$ -\Delta u+ u=u^{2^*-1}+\lambda u^{q-1}
\quad {\rm in} \ \ \mathbb{R}^N, $$ where $N\ge 3$ is an integer,
$2^*=\frac{2N}{N-2}$ is the Sobolev critical exponent, $2<q<2^*$ and
$\lambda>0$ is a parameter. It is known that as $\lambda\to 0$, after a
rescaling the ground state solutions of the equation converge to a particular
solution of the critical Emden-Fowler equation $-\Delta u=u^{2^*-1}$. We
establish a sharp asymptotic characterisation of such a rescaling, which
depends in a non-trivial way on the space dimension $N=3$, $N=4$ or $N\ge 5$.

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The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci