Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normalized ground states for the NLS equation with combined
  nonlinearities   We study existence and properties of ground states for the nonlinear
Schr\"odinger equation with combined power nonlinearities \[ -\Delta u= \lambda
u + \mu |u|^{q-2} u + |u|^{p-2} u \qquad \text{in $\mathbb{R}^N$, $N \ge 1$,}
\] having prescribed mass \[ \int_{\mathbb{R}^N} |u|^2 = a^2. \] Under
different assumptions on $q<p$, $a>0$ and $\mu \in \mathbb{R}$ we prove several
existence and stability/instability results. In particular, we consider cases
when \[ 2<q \le 2+ \frac{4}{N} \le p<2^*, \quad q \neq p, \] i.e. the two
nonlinearities have different character with respect to the $L^2$-critical
exponent. These cases present substantial differences with respect to purely
subcritical or supercritical situations, which were already studied in the
literature.
  We also give new criteria for global existence and finite time blow-up in the
associated dispersive equation.

22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom